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2016-‐‑2017 Math Nation Geometry Scope & Sequence: MAFS Topics and Standards Alignment

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TABLE OF CONTENTS

SECTIONS PAGES IN THIS DOC

Section 1: Introduction to Geometry – Points, Lines and Planes 2-‐3

Section 2: Introduction to Geometry – Transformations and Constructions 4-‐7

Section 3: Angles 8-‐10

Section 4: Introduction to Polygons – Part 1 11-‐13

Section 5: Introduction to Polygons – Part 2 14-‐15

Section 6: Triangles – Part 1 16-‐17

Section 7: Triangles – Part 2 18-‐19

Section 8: Right Triangles 20-‐22

Section 9: Quadrilaterals – Part 1 23-‐25

Section 10: Quadrilaterals – Part 2 25-‐27

Section 11: Properties of 𝑁-‐gons 28-‐30

Section 12: Circles – Part 1 31-‐34

Section 13: Circles – Part 2 35-‐36

Section 14: Three Dimensional Geometry 37-‐39

Section 15: Additional Modeling with Geometry



SECTION 1: INTRODUCTION TO GEOMETRY – POINTS, LINES AND PLANES

Section 1, Topic 1: Basics of Geometry – Part 1

MAFS.912.G-CO.1.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.

This topic focuses on defining and representing points, lines, line segments, planes, rays, and angles, as the building

blocks of Geometry.

Section 1, Topic 2: Basics of Geometry – Part 2


This topic is the second part of defining and representing points, lines, line

segments, planes, rays, and angles, as the building blocks of Geometry.

Section 1, Topic 3: Midpoint and Distance in the Coordinate Plane

– Part 1

MAFS.912.G-CO.1.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. MAFS.912.G-GPE.2.6 Find the point on a given line segment between two given points that partitions a segment in a given ratio. MAFS.912.G-GPE.2.7 Use coordinates to compute the perimeter of polygons and areas of triangles and rectangles.

This topic focuses on midpoint and distance, and applications on a

coordinate plane by either finding midpoint coordinates, endpoint

coordinates or length of segments.

Section 1, Topic 4: Midpoint and Distance in the Coordinate Plane

– Part 2

MAFS.912.G-CO.1.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. MAFS.912.G-GPE.2.6 Find the point on a given line segment between two given points that partitions a segment in a given ratio. MAFS.912.G-GPE.2.7 Use coordinates to compute the perimeter of polygons and areas of triangles and rectangles.

This topic teaches students how to use the commutative and associative properties to

identify equivalent expressions. Students will determine which properties (distribute, associative, and commutative) have been used when writing equivalent expressions.



Section 1, Topic 5: Partitioning a Line Segment – Part 1

MAFS.912.G-GPE.2.6 Find the point on a directed line segment between two given points that partitions the segment in a given ratio.

This topic focuses on finding the point on a directed line segment between two given

points that partitions the segment in a given ratio.

Section 1, Topic 6: Partitioning a Line Segment – Part 2

MAFS.912.G-GPE.2.6 Find the point on a directed line segment between two given points that partitions the segment in a given ratio.

This topic is the second part on finding the point on a directed line segment between

two given points that partitions the segment in a given ratio.

Section 1, Topic 7: Parallel and Perpendicular Lines – Part 1

MAFS.912.G-CO.1.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. MAFS.912.G-GPE.2.5 Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems.

This topic focuses on identifying parallel and perpendicular lines, and writing

equations of lines parallel or perpendicular to another line.

Section 1, Topic 8: Parallel and Perpendicular Lines – Part 2

MAFS.912.G-CO.1.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. MAFS.912.G-GPE.2.5 Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems.

This topic is the second part on identifying parallel and perpendicular lines, and writing equations of lines parallel or

perpendicular to another line.



SECTION 2: INTRODUCTION TO GEOMETRY – TRANSFORMATIONS AND CONSTRUCTIONS

Section 2, Topic 1: Introduction to Transformations

MAFS.912.G-CO.1.2 Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not. MAFS.912.G-CO.1.4 Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments. MAFS.912.G-CO.1.5 Given a geometric figure and a rotation, reflection, or translation, draw the transfoemed figure. Specify a sequence of transformations that will carry a given figure onto itself.

This topic focuses on introducing rigid and non-rigid transformations, translation,

reflection, rotation, and dilation.

Section 2, Topic 2: Examining and Using Translations


This topic focuses on performing translations of points and line segments on

a coordinate plane.



Section 2, Topic 3: Examining and Using Dilations – Part 1


This topic focuses on performing dilations of points and line segments on a

coordinate plane.

Section 2, Topic 4: Examining and Using Dilations – Part 2


This topic focuses on performing dilations of points and line segments on a

coordinate plane.



Section 2, Topic 5: Examining and Using Rotations

MAFS.912.G-CO.1.2 Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not. MAFS.912.G-CO.1.4 Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments. MAFS.912.G-CO.1.5 Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure. Specify a sequence of transformations that will carry a given figure onto itself.

This topic focuses on performing rotation of points and line segments on a coordinate

plane.

Section 2, Topic 6: Examining and Using Reflections

MAFS.912.G-CO.1.2 Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not. MAFS.912.G-CO.1.4 Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments. MAFS.912.G-CO.1.5 Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure. Specify a sequence of transformations that will carry a given figure onto itself.

This topic focuses on performing reflection of points and line segments on a

coordinate plane.



Section 2, Topic 7: Basic Constructions – Part 1

MAFS.912.G-CO.4.12 Make formal geometric constructions with a variety of tools and methods. Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.

This topic focuses on constructions of line segments.

Section 2, Topic 8: Basic Constructions – Part 2

MAFS.912.G-CO.4.12 Make formal geometric constructions with a variety of tools and methods. Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.

This topic follows up the previous one on constructions, but it focuses on

perpendicular bisectors.



SECTION 3: ANGLES

Section 3, Topic 1: Introduction to Angles – Part 1


This topic focuses on how to measure and classify an angle.

Section 3, Topic 2: Introduction to Angles – Part 2


This topic follows up on how to measure and classify an angle.

Section 3, Topic 3: Angle Pairs – Part 1

MAFS.912.G-CO.3.9 Prove theorems about lines and angles; use theorems about lines and angles to solve problems.

This topic focuses on angle pairs, linear pairs, adjacent angles, and vertical angles. It also

introduces the concept of an, angle bisector. The Linear Pair Postulate, the

Congruent Complements Theorem, the Congruent Supplement Theorem, and the Right Angles Theorem are also introduced.

Section 3, Topic 4: Angle Pairs – Part 2

MAFS.912.G-CO.3.9 Prove theorems about lines and angles; use theorems about lines and angles to solve problems.

This topic follows up on angle pairs, linear pairs, adjacent angles, and vertical angles. It

also provides practice exercises on tangle bisectors, the Linear Pair Postulate, the Congruent Complements Theorem, the

Congruent Supplement Theorem, and the Right Angles Theorem.

Section 3, Topic 5: Special Types of Angle Pairs Formed by

Transversals and Non-Parallel Lines

MAFS.912.G-CO.1.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. MAFS.912.G-CO.3.9 Prove theorems about lines and angles; use theorems about lines and angles to solve problems.

This topic focuses on discussing the special Types of angle pairs formed by transversals

and non-parallel lines.



Section 3, Topic 6: Special Types of Angle Pairs Formed by Transversals and Parallel Lines – Part 1


This topic focuses on the relationship between angle pairs when the transversal

cut two parallel lines.

Section 3, Topic 7: Special Types of Angle Pairs Formed by Transversals and Parallel Lines – Part 2


This topic is the second part on the relationship between angle pairs when the

transversal cut two parallel lines.

Section 3, Topic 8: Perpendicular Transversals


This topic focuses on transversals that perpendicular to 2 or more lines.

Section 3, Topic 9: Angle-Preserving Transformations

MAFS.912.G-CO.1.2 Compare transformations that preserve distance and angle to those that do not. MAFS.912.G-CO.1.4 Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines and line segments.

This topic focuses on applying transformations to figures formed by parallel

lines crossed by a transversal. Most importantly, it focuses on angle-preserving

transformations.



MAFS.912.G-CO.1.5 Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure. MAFS.912.G-CO.3.9 Prove theorems about angles and use theorems about angles and lines to solve problems.

Section 3, Topic 10: Constructions of Angles, Perpendicular Lines,

and Parallel Lines

MAFS.912.G-CO.4.12 Make formal geometric constructions with a variety of tools and methods. Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines,

This topic focuses on constructions of parallel and perpendicular lines.



SECTION 4: INTRODUCTION TO POLYGONS – PART 1

Section 4, Topic 1: Introduction to Polygons – Part 1

MAFS.912.G-MG.1.1 Use geometric shapes, their measures, and their properties to describe objects. MAFS.912.G-CO.3.10 Prove theorems about triangles. Use theorems about triangles to solve problems: measures of interior angles of a triangle sum to 180.

This topic introduces polygons and it compares and contrasts regular and irregular polygons, convex and concave polygons, and simple

and complex polygons.

Section 4, Topic 2: Introduction to Polygons – Part 2

MAFS.912.G-MG.1.1 Use geometric shapes, their measures, and their properties to describe objects. MAFS.912.G-CO.3.10 Prove theorems about triangles. Use theorems about triangles to sovle problems: measures of interior angles of a triangle sum to 180.

This topic is the second part on introducing polygons, comparing and contrasting regular and irregular polygons, convex and concave polygons, and simple and complex polygons.

Section 4, Topic 3: Angles of Polygons

MAFS.912.G-CO.1.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. MAFS.912.G-MG.1.1 Use geometric shapes, their measures, and their properties to describe objects.

This topic focuses on measuring the interior and exterior angles of regular and irregular

polygons.

Section 4, Topic 4: Translation of Polygons

MAFS.912.G-CO.1.2 Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not. MAFS.912.G-CO.1.4 Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines and line segments.

This topic focuses on performing translations of polygons on a coordinate plane and finding the coordinates or location of the image and

the pre-image.



MAFS.912.G-CO.1.5 Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure. Specify a sequence of transformations that will carry a given figure onto itself.

Section 4, Topic 5: Reflection of Polygons

MAFS.912.G-CO.1.2 Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not. MAFS.912.G-CO.1.4 Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines and line segments. MAFS.912.G-CO.1.5 Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure. Specify a sequence of transformations that will carry a given figure onto itself.

This topic focuses on performing reflections of polygons on a coordinate plane and finding the coordinates or location of the image and

the pre-image.

Section 4, Topic 6: Rotation of Polygons – Part 1

MAFS.912.G-CO.1.2 Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not. MAFS.912.G-CO.1.4 Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines and line segments. MAFS.912.G-CO.1.5 Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure. Specify a sequence of

This topic focuses on performing rotations of polygons on a coordinate plane and finding the coordinates or location of the image and

the pre-image.



transformations that will carry a given figure onto itself.

Section 4, Topic 7: Rotation of Polygons – Part 2

MAFS.912.G-CO.1.2 Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not. MAFS.912.G-CO.1.4 Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines and line segments. MAFS.912.G-CO.1.5 Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure. Specify a sequence of transformations that will carry a given figure onto itself.

This is the second part of the set of topics focusing on performing rotations of polygons

on a coordinate plane and finding the coordinates or location of the image and the

pre-image.

Section 4, Topic 8: Dilation of Polygons

MAFS.912.G-CO.1.2 Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not. MAFS.912.G-SRT.1.1 Verify experimentally the properties of dilations given by a center and a scale factor: a. A dilation takes a line not passing through the center of the dilation to a parallel line and leaves a line passing through the center unchanged. b. The dilation of a line segment is longer or shorter in the raitio given by the scale factor.

This topic focuses on performing dilations of polygons on a coordinate plane and finding the coordinates or location of the image and

the pre-image.



SECTION 5: INTRODUCTION TO POLYGONS – PART 2

Section 5, Topic 1: Compositions of Transformations of Polygons –

Part 1


This topic focuses on discussing the different compositions of transformations such as glide reflection, double reflection, and composition

of isometries.

Section 5, Topic 2: Compositions of Transformations of Polygons –

Part 2


This topic is the second part on discussing the different compositions of transformations such

as glide reflection, double reflection, and composition of isometries.

Section 5, Topic 3: Symmetries of Regular Polygons

MAFS.912.G-CO.1.3 Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself. MAFS.912.G-CO.1.5 Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure. Specify a sequence of transformations that will carry a given figure onto itself.

This topic focuses on discussing reflections and rotations that carry a geometric figure onto

itself.

Section 5, Topic 4: Congruence and Similarity of Polygons – Part 1

MAFS.912.G-CO.2.6 Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent. MAFS.912.G-CO.2.7 Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent. MAFS.912.G-SRT.1.2 Given two figures, use the definition of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for

This topic focuses on distinguishing between transformations that produce congruent

images and transformations that produce similar images.



triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.

Section 5, Topic 5: Congruence and Similarity of Polygons – Part 2

MAFS.912.G-CO.2.6 Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent. MAFS.912.G-CO.2.7 Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent. MAFS.912.G-SRT.1.2 Given two figures, use the definition of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.

This topic focuses on distinguishing between transformations that produce congruent

images and transformations that produce similar images.



SECTION 6: TRIANGLES – PART 1

Section 6, Topic 1:

Introduction to Triangles – Part 1

MAFS.912.G-CO.3.10 Prove theorems about triangles; use theorems about triangles to solve problems. MAFS.912.G-GPE.2.5 Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems.

This topic focuses on classifying triangles by sides and angles, and using triangles’

characteristics to find missing sides, angles or to apply algebraic skills. It also proves the Triangle

Sum theorem.

Section 6, Topic 2: Introduction to Triangles – Part 2

MAFS.912.G-CO.3.10 Prove theorems about triangles; use theorems about triangles to solve problems. MAFS.912.G-GPE.2.5 Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems.

This topic offers more opportunities for practicing on classifying triangles by sides and angles, and using triangles’ characteristics to

find missing sides, angles or to apply algebraic skills. It also proves the Triangle Sum theorem.

Section 6, Topic 3: Area and Perimeter on the Coordinate Plane –

Part 1

MAFS.912.G-GPE.2.7 Use coordinates to computer perimeters of polygons and areas of triangles and rectangles.

This topic focuses on calculating area and perimeter of a triangle, and using perimeter

and area to find missing sides.

Section 6, Topic 4: Area and Perimeter on the Coordinate Plane –

Part 2

MAFS.912.G-GPE.2.7 Use coordinates to computer perimeters of polygons and areas of triangles and rectangles.

This topic offers more opportunities for practicing on calculating area and perimeter of a triangle, and using perimeter and area to

find missing sides.

Section 6, Topic 5: Triangle Congruence – SSS and SAS – Part 1

MAFS.912.G-CO.2.8 Explain how the criteria for triangle congruence (ASA, SAS, SSS, and Hypotenuse Leg) follow from the definition of congruence in terms of rigid motions. MAFS.912.G-SRT.2.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figure.

This topic guides students through the method of using Side-Side-Side and Side-Angle-Side theorems to find missing sides or angles, and to prove certain characteristics of triangles.

Section 6, Topic 6: Triangle Congruence – SSS and SAS – Part 2

MAFS.912.G-CO.2.8 Explain how the criteria for triangle congruence (ASA, SAS, SSS, and Hypotenuse Leg) follow from the definition of congruence in terms of rigid motions.

This topic keeps on guiding students through the method of using Side-Side-Side and Side-Angle-Side theorems to find missing sides or angles, and to prove certain characteristics of triangles.



MAFS.912.G-SRT.2.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figure.

Section 6, Topic 7: Triangle Congruence – ASA and AAS – Part 1

MAFS.912.G-CO.2.8 Explain how the criteria for triangle congruence (ASA, SAS, SSS, and Hypotenuse Leg) follow from the definition of congruence in terms of rigid motions. MAFS.912.G-SRT.2.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

This topic guides students through the method of using Angle-Side-Angle and Angle-Angle-Side theorems to find missing sides or angles,

and to prove certain characteristics of triangles.

Section 6, Topic 8: Triangle Congruence – ASA and AAS – Part 2


This topic keeps on guiding students through the method of using Angle-Side-Angle and

Angle-Angle-Side theorems to find missing sides or angles, and to prove certain characteristics

of triangles.

Section 6, Topic 9: Using Triangle Congruency to Find Missing

Variables


This topic focuses on using triangle congruency

theorems to find missing sides by using algebraic skills.



SECTION 7: TRIANGLES – PART 2

Section 7, Topic 1: Triangle Similarity – Part 1

MAFS.912.G-SRT.1.2: Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides. MAFS.912.G-SRT.1.3 Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar. MAFS.912.G-SRT.2.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

This topic guides students through different triangle similarity criteria to prove that two

triangles are similar or certain lengths of two triangles are similar.

Section 7, Topic 2: Triangle Similarity – Part 2

MAFS.912.G-SRT.1.2: Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides. MAFS.912.G-SRT.1.3 Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar. MAFS.912.G-SRT.2.4 Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity.

This topic keeps on guiding students through different triangle similarity criteria to prove that

two triangles are similar or certain lengths of two triangles are similar.



MAFS.912.G-SRT.2.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

Section 7, Topic 3: Triangle Midsegment Theorem – Part 1

MAFS.912.G-CO.3.10 Prove theorems about triangles; use theorems about triangles to solve problems.

This topic focuses on understanding and applying the Triangle Midsegment Theorem.

Section 7, Topic 4: Triangle Midsegment Theorem – Part 2


This topic keeps focusing on understanding and applying the Triangle Midsegment

Theorem.

Section 7, Topic 5: Triangle Inequalities


This topic introduces the Triangle Inequality Theorem, the Hinge Theorem and the

Converse of the Hinge Theorem,

Section 7, Topic 6: More Triangle Proofs


This topic wraps up all the theorems introduced this section and use them to prove different

features of triangles. Section 7, Topic 7:

Inscribed and Circumscribed Circles of Triangles

MAFS.912.G-C.1.3 Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.

This topic focuses on constructing triangles and it reviews incircle, circumcircle and circumcenter based on a triangle.

Section 7, Topic 8: Medians of a Triangle

MAFS.912.G-CO.3.10 Prove theorems about triangles; use theorems about triangles to solve problems. MAFS.912.G-GPE.2.4 Use coordinates to prove simple geometric theorems algebraically.

This topic focuses on medians in a triangle, the lengths of medians and the ratio of the length from the vertex to the centroid to the length from the centroid to the midpoint of the side.



SECTION 8: RIGHT TRIANGLES AND INTRODUCTION TO TRIGONOMETRY

Section 8, Topic 1: The Pythagorean Theorem

MAFS.912.G-SRT.3.8 Use trigonometric ratios and Pythagorean Theorem to solve right triangles in applied problems. MAFS.912.G-SRT.2.4 Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity.

This topic introduces the Pythagorean Theorem and Pythagorean triples and focuses on its

applications

Section 8, Topic 2: The Converse of the Pythagorean Theorem

MAFS.912.G-SRT.3.8 Use trigonometric ratios and Pythagorean Theorem to solve right triangles in applied problems.

This topic introduces Converse of the Pythagorean Theorem and focuses on its

applications.

Section 8, Topic 3: Proving Right Triangles Congruent

MAFS.912.G-CO.2.8 Explain how the criteria for triangle congruence (ASA, SAS, SSS, and Hypotenuse-Leg) follow from the definition of congruence in terms of rigid motions. MAFS.912.G-CO.3.10 Prove theorems about triangles; use theorems about triangles to solve problems.

This topic teaches us the Hypotenuse-Leg Theorem to prove right triangles congruent.

Section 8, Topic 4: Special Right Triangles: 45-45-90

MAFS.912.G-CO.3.10 Prove theorems about triangles; use theorems about triangles to solve problems. MAFS.912.G-SRT.3.8 Use trigonometric ratios and Pythagorean Theorem to solve right triangles in applied problems.

This topic focuses on using the features of 45-45-90 right triangles to solve problems.

Section 8, Topic 5: Special Right Triangles: 30-60-90

MAFS.912.G-SRT.3.8 Use trigonometric ratios and Pythagorean Theorem to solve right triangles in applied problems.

This topic focuses on using the features of 30-60-90 right triangles to solve problems.

Section 8, Topic 6: Right Triangles Similarity – Part 1

MAFS.912.G-SRT.1.2 Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the

This topic introduces the Right Triangle Altitude Theorem and Geometric Mean theorems to

work with similar right triangles.



meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides. MAFS.912.G-SRT.2.4 Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity. MAFS.912.G-SRT.2.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. MAFS.912.G-SRT.3.6 Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.

Section 8, Topic 7: Right Triangles Similarity – Part 2

MAFS.912.G-SRT.1.2 Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides. MAFS.912.G-SRT.2.4 Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity.

This topic is the second part on working with similar right triangles, but with more

applications problems.



MAFS.912.G-SRT.2.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. MAFS.912.G-SRT.3.6 Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.

Section 8, Topic 8: Introduction to Trigonometry – Part 1

MAFS.912.G-SRT.3.7 Explain and use the relationship between the sine and cosine of complementary angles. MAFS.912.G-SRT.3.8 Use trigonometric ratios and Pythagorean Theorem to solve right triangles in applied problems.

This topic introduces trigonometric ratios and functions to use when finding a missing side or

a missing angle in a right triangle.

Section 8, Topic 9: Introduction to Trigonometry – Part 2

MAFS.912.G-SRT.3.7 Explain and use the relationship between the sine and cosine of complementary angles. MAFS.912.G-SRT.3.8 Use trigonometric ratios and Pythagorean Theorem to solve right triangles in applied problems.

This topic is the second part of the introduction of trigonometric ratios and functions to use

when finding a missing side or a missing angle in a right triangle.



SECTION 9: QUADRILATERALS – PART 1

Section 9, Topic 1: Introduction to Quadrilaterals – Part 1

MAFS.912.G-CO.1.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. MAFS.912.G-CO.3.11 Prove theorems about parallelograms; use theorems about parallelograms to solve problems. MAFS.912.G-MG.1.1 Use geometric shapes, their measures and their properties to describe objects.

This topic introduces the properties and characteristics of quadrilateral, and

distinguishing between different types of quadrilaterals.


MAFS.912.G-CO.1.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. MAFS.912.G-CO.3.11 Prove theorems about parallelograms; use theorems about parallelograms to solve problems. MAFS.912.G-MG.1.1 Use geometric shapes, their measures and their properties to describe objects. MAFS.912.G-GPE.2.4 Use coordinates to prove simple geometric theorems algebraically, for example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle.

This topic is the second part on exploring the properties and characteristics of quadrilateral,

using coordinates to distinguish between different types of quadrilaterals, and finding

area and perimeter.


MAFS.912.G-CO.1.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined

This topic is the third part on exploring and mostly applying the properties and

characteristics of quadrilateral.



notions of point, line, distance along a line, and distance around a circular arc. MAFS.912.G-CO.3.11 Prove theorems about parallelograms; use theorems about parallelograms to solve problems. MAFS.912.G-MG.1.1 Use geometric shapes, their measures and their properties to describe objects. MAFS.912.G-GPE.2.4 Use coordinates to prove simple geometric theorems algebraically, for example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle.

Section 9, Topic 4: Parallelograms – Part 1

MAFS.912.G-CO.1.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. MAFS.912.G-CO.3.11 Prove theorems about parallelograms; use theorems about parallelograms to solve problems.

This topic focuses on using theorems of parallelograms to solve problems or prove

certain characteristics or relationships in quadrilaterals.

Section 9, Topic 5: Parallelograms – Part 2


This topic is the second part on on using theorems of parallelograms to solve problems or prove certain characteristics or relationships

in quadrilaterals.

Section 9, Topic 6: Rectangles and Squares – Part 1

MAFS.912.G-CO.1.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined

This topic focuses on using properties and theorems of rectangles to solve problems or



notions of point, line, distance along a line, and distance around a circular arc. MAFS.912.G-CO.3.11 Prove theorems about parallelograms; use theorems about parallelograms to solve problems.

prove certain characteristics or relationships in quadrilaterals.

Section 9, Topic 7: Rectangles and Squares – Part 2


This topic focuses on using properties and theorems of squares and rhombi to solve

problems or prove certain characteristics or relationships in quadrilaterals.



SECTION 10: QUADRILATERALS – PART 2

Section 10, Topic 1: Rhombi


This topic focuses on using properties and theorems of rhombi, specifically, to solve

problems or prove certain characteristics or relationships in quadrilaterals.

Section 10, Topic 2: Kites

MAFS.912.G-CO.1.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. MAFS.912.G-MG.1.1 Use geometric shapes, their measures and their properties to describe objects.

This topic focuses on using properties and theorems of kites to solve problems or prove

certain characteristics or relationships in quadrilaterals.

Section 10, Topic 3: Trapezoids


This topic focuses on using properties and theorems of trapezoids to solve problems or


Section 10, Topic 4: Midsegment of Trapezoids


This topic focuses on using the Midsegment theorem for trapezoids to solve problems or




Section 10, Topic 5: Quadrilaterals in Coordinate Geometry – Part 1

MAFS.912.G-CO.1.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. MAFS.912.G-GPE.2.4 Use coordinates to prove simple geometric theorems algebraically. MAFS.912.G-GPE.2.7 Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.

This topic revisits the distance formula, midpoint formula and slope formula to use

when developing coordinate geometry proofs for quadrilaterals and identifying different

types of quadrilaterals based on the coordinates of their vertices.

Section 10, Topic 6: Quadrilaterals in Coordinate Geometry – Part 2

MAFS.912.G-CO.1.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. MAFS.912.G-CO.3.11 Students will prove theorems about parallelograms. Students will use properties of parallelograms to solve problems. MAFS.912.G-GPE.2.4 Use coordinates to prove simple geometric theorems algebraically. MAFS.912.G-GPE.2.7 Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.

This topic continue to revisit the distance formula, midpoint formula and slope formula to

use when developing coordinate geometry proofs for quadrilaterals and identifying

different types of quadrilaterals based on the coordinates of their vertices.

Section 10, Topic 7: Constructions of Quadrilaterals

MAFS.912.G-CO.4.12 Make formal geometric constructions with a variety of tools and methods. MAFS.912.G-CO.4.13 Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.

This topic focuses on constructing quadrilaterals such as rectangles, kites and trapezoids. It also emphasizes on how to use construction techniques to make sure all the properties of the quadrilaterals are evident in

the constructions.



SECTION 11: Properties of 𝑵-gons

Section 11, Topic 1: Introduction of 𝑁-gons – Part 1

MAFS.912.G-GPE.2.7 Use coordinates to computer perimeter and areas of polygons, triangles and rectangles. (In items that require students to find the area, the polygon must be able to be divided into triangles or rectangles.) MAFS.912.G-MG.1.1 Use geometric shapes. their measures, and their properties to describe objects. MAFS.912.G-SRT.2.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

The topic introduces polygons with more than 4 sides, and explores the different features of

these polygons as well as ways to break them into polygons with 3 or 4 sides.

Section 11, Topic 2: Introduction of 𝑁-gons – Part 2

MAFS.912.G-GPE.2.7 Use coordinates to computer perimeter and areas of polygons, triangles and rectangles. (In items that require students to find the area, the polygon must be able to be divided into triangles or rectangles.) MAFS.912.G-MG.1.1 Use geometric shapes. their measures, and their properties to describe objects. MAFS.912.G-SRT.2.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

The topic continues to explore the different features of polygons with more than 4 sides, as well as strategies to find area and perimeter.

Section 11, Topic 3: Angles of 𝑁-gons – Part 1

MAFS.912.G-CO.1.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. MAFS.912.G-MG.1.1 Use geometric shapes. their measures, and their properties to describe objects.

This topic focuses on calculating the base angles and interior angles of regular polygons

with more than 4 sides.



MAFS.912.G-SRT.2.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

Section 11, Topic 4: Angles of 𝑁-gons – Part 2

MAFS.912.G-CO.1.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. MAFS.912.G-MG.1.1 Use geometric shapes. their measures, and their properties to describe objects. MAFS.912.G-SRT.2.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

This topic focuses on calculating the exterior angles of regular polygons with more than 4

sides, and angles of irregular polygons.

Section 11, Topic 5: Segments in regular 𝑁-gons – Part 1

MAFS.912.G-MG.1.1 Use geometric shapes. their measures, and their properties to describe objects. MAFS.912.G-MG.1.3 Apply geometric methods to solve design problems.

This topic focuses on finding diagonals, diameters, radius and apothem in polygons

with more than 4 sides.

Section 11, Topic 6: Segments in regular 𝑁-gons – Part 2

MAFS.912.G-MG.1.1 Use geometric shapes. their measures, and their properties to describe objects. MAFS.912.G-MG.1.3 Apply geometric methods to solve design problems.

This topic focuses on finding side, radius and apothem in polygons with more than 4 sides

using trigonometry.

Section 11, Topic 7: Area of 𝑁-gons

MAFS.912.G-GPE.2.7 Use coordinates to compute perimeters of polygons and areas of triangles and rectangles. MAFS.912.G-MG.1.3 Apply geometric methods to solve design problems. MAFS.912.G-MG.1.1 Use geometric shapes, their measures, and their properties to describe objects.

This topic focuses on finding the area of regular and irregular polygons with more than 4 sides.



MAFS.912.G-SRT.2.5 Use congruence criteria for triangles to solve problems and prove geometric relationships.

Section 11, Topic 8: Coordinate Geometry – Part 1

MAFS.912.G-GPE.2.4 Use coordinates to prove simple geometric theorems algebraically. MAFS.912.G-GPE.2.7 Use coordinates to compute perimeters of polygons and areas of triangles and rectangles. MAFS.912.G-MG.1.1 Use geometric shapes, their measures, and their properties to describe objects.

This topic focuses on using coordinate geometry to classify polygons with more than 4

sides.

Section 11, Topic 9: Coordinate Geometry – Part 2

MAFS.912.G-GPE.2.4 Use coordinates to prove simple geometric theorems algebraically. MAFS.912.G-GPE.2.7 Use coordinates to compute perimeters of polygons and areas of triangles and rectangles. MAFS.912.G-MG.1.1 Use geometric shapes, their measures, and their properties to describe objects.

This topic focuses on using coordinate geometry to classify polygons with more than 4

sides.



SECTION 12: CIRCLES – PART 1

Section 12, Topic 1: Circumference of a Circle

MAFS.912.G-C.1.2 Identify and describe relationships among inscribed angles, radii, and chords. Include the relationships between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle. {Items may include finding or describing the length of arcs when given information.} MAFS.912.G-GMD.1.1 Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a circle, pyramid and cone.

This topic focuses on calculating and using the circumference of a circle to solve problems.

Section 12, Topic 2: Arcs and Circumference of a Circle

MAFS.912.G-C.1.2 Identify and describe relationships among inscribed angles, radii, and chords. Include the relationships between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle. {Items may include finding or describing the length of arcs when given information.} MAFS.912.G-GMD.1.1 Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a circle, pyramid and cone.

This topic focuses on calculating and using the circumference of a circle to solve problems.

Section 12, Topic 3: Area of a Circle

MAFS.912.G-C.1.2 Identify and describe relationships among inscribed angles, radii, and chords. Include the relationships between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle. {Items may include finding or describing the length of arcs when given information.}

This topic focuses on calculating and using the

area of a circle to solve problems.



MAFS.912.G-GMD.1.1 Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a circle, pyramid and cone.

Section 12, Topic 4: Sectors of a Circle

MAFS.912.G-C.1.2 Identify and describe relationships among inscribed angles, radii, and chords. Include the relationships between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle. {Items may include finding or describing the length of arcs when given information.} MAFS.912.G-C.2.5 Derive the formula for the area of a sector. MAFS.912.G-GMD.1.1 Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a circle, pyramid and cone.

This topic focuses on calculating and using the area of a circle and sectors to solve problems.

Section 12, Topic 5: Circles in the Coordinate Plane: Standard Form

MAFS.912.G-C.1.2 Identify and describe relationships among inscribed angles, radii, and chords. Include the relationships between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle. MAFS.912.G-GPE.1.1 Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the the center and radius of a circle given by an equation.

In this topic, students learn how derive and apply the equation of a circle in standard form

on a coordinate plane.



MAFS.912.G-GPE.2.4 Use coordinates to prove simple geometric theorems algebraically.

Section 12, Topic 6: Circles in the Coordinate Plane: General Form

MAFS.912.G-C.1.2 Identify and describe relationships among inscribed angles, radii, and chords. Include the relationships between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle. MAFS.912.G-GPE.1.1 Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the the center and radius of a circle given by an equation. MAFS.912.G-GPE.2.4 Use coordinates to prove simple geometric theorems algebraically.

In this topic, students learn how derive and apply the equation of a circle in general form

on a coordinate plane.

Section 12, Topic 7: Circle Transformations

MAFS.912.G-C.1.1 Prove that all circles are similar. MAFS.912.G-CO.1.2 Represent transformations in the plane, describe transformations as functions that take points in the plane as inputs and give points as outputs. Compare transformations that preserve distance and angle to those that do not. MAFS.912.G-SRT.1.1 Verify experimentally the proportions of dilations given by a center and a scale factor.

This topic focuses on understanding how to transform circles, especially dilating a circle

centered at the origin or centered on another point.

Section 12, Topic 8: Radians and Degrees

MAFS.912.G-C.1.2 Identify and describe relationships among inscribed angles, radii, and chords. Include the relationships between central, inscribed, and circumscribed angles;

This topic focuses on converting from radians to degree, and from degrees to radians, and

understanding the applications of radians and degrees.



inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle. {Items may include finding or describing the length of arcs when given information.} MAFS.912.G-C.2.5 Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector.



SECTION 13: CIRCLES – PART 2

Section 13, Topic 1: Arcs and Inscribed Angles – Part 1

MAFS.912.G-C.1.2 Identify and describe relationships among inscribed angles, radii, and chords. Include the relationships between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle.

This topic focuses on discovering and applying inscribed angles conjectures to solve problems.

Section 13, Topic 2: Arcs and Inscribed Angles – Part 2


This topic is the second part on discovering and applying inscribed angles conjectures to

solve problems.

Section 13, Topic 3: Inscribed Polygons in a Circle

MAFS.912.G-C.1.3 Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle. MAFS.912.G-CO.4.13 Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.

This topic focuses on exploring and using properties of a cyclic quadrilateral and other

polygons inscribed in a circle.

Section 13, Topic 4: Constructing Inscribed Polygons in a Circle


This topic focuses on constructing an equilateral triangle, a square, and a regular

hexagon inscribed in a circle.

Section 13, Topic 5: Tangent Lines, Secants and Chords – Part 1

MAFS.912.G-C.1.2 Identify and describe relationships among inscribed angles, radii, and chords. Include the relationships between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right

This topic focuses on proving and applying properties and theorems about tangent lines,

secants and chords. Theorems include the Tangent theorem and the Tangent Segment

theorem.



angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle.

Section 13, Topic 6: Tangent Lines, Secants and Chords – Part 2


This topic keeps focusing on proving and applying properties and theorems about

tangent lines, secants and chords. Theorems include the perpendicular-to-a-chord

theorem. chords distance to center theorem, and intersecting chords theorem.

Section 13, Topic 7: Circumscribed Angles and Beyond – Part 1


This topic focuses on identifying and calculating tangent-chord angles and

circumscribed angles.

Section 13, Topic 8: Circumscribed Angles and Beyond – Part 2


This topic keeps identifying and calculating tangent-chord angles and circumscribed

angles.

Section 13, Topic 9: Constructing Inscribed and Circumscribed

Circles of Triangles


This topic focuses on constructing inscribed and circumscribed circles on a triangle.



SECTION 14: THREE DIMENSIONAL GEOMETRY

Section 14, Topic 1: Geometry Nets and Three Dimensional Figures

MAFS.912.G-GMD.1.1 Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone.

This topic focuses on understanding how to unfold a geometric solid into a geometry nets and vice versa, including the discussion of the

different components of the nets.

Section 14, Topic 2: Cavalieri’s Principle for Area

MAFS.912.G-GMD.1.1 Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. MAFS.912.G-MG.1.1 Use geometric shapes, their measures, and their properties to describe objects.

This topic focuses on the 2-dimensional and 3-dimensional case for the use of the Cavalieri’s

Principle to estimate area.

Section 14, Topic 3: Cavalieri’s Principle for Volume

MAFS.912.G-GMD.1.1 Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. MAFS.912.G-GMD.2.4 Identify the shapes of two-dimensional cross-sections of three-dimensional objects and identify three-dimensional objects generated by rotations of two-dimensional objects. MAFS.912.G-MG.1.1 Use geometric shapes, their measures, and their properties to describe objects.

This topic focuses on the 3-dimensional case for the use of the Cavalieri’s Principle to estimate

volume.

Section 14, Topic 4: Volume of Prisms and Cylinders

MAFS.912.G-GMD.1.3 Use volume for cylinders, pyramids, cones, and spheres to sovle problems. MAFS.912.G-MG.1.1 Use geometric shapes, their measures, and their properties to describe objects. MAFS.912.G-MG.1.2 Apply concepts of density based on area and volume in modeling situations.

This topic focuses on understanding, calculating and applying the volume of prisms and

cylinders.



Section 14, Topic 5: Surface Area of Prisms and Cylinders

MAFS.912.G-MG.1.1 Use geometric shapes, their measures, and their properties to describe objects. MAFS.912.G-MG.1.2 Apply concepts of density based on area and volume in modeling situations.

This topic focuses on understanding, calculating and applying the lateral area and surface area

of prisms and cylinders.

Section 14, Topic 6: Volume of Pyramids and Cones

MAFS.912.G-GMD.1.3 Use volume for cylinders, pyramids, cones, and spheres to sovle problems. MAFS.912.G-MG.1.1 Use geometric shapes, their measures, and their properties to describe objects. MAFS.912.G-MG.1.2 Apply concepts of density based on area and volume in modeling situations.

This topic focuses on understanding, calculating and applying the volume of pyramids and

cones.

Section 14, Topic 7: Surface Area of Pyramids and Cones

MAFS.912.G-MG.1.1 Use geometric shapes, their measures, and their properties to describe objects.

This topic focuses on understanding, calculating and applying the lateral area and surface area

of pyramids and cones.

Section 14, Topic 8: Spheres

MAFS.912.G-GMD.1.3 Use volume for cylinders, pyramids, cones, and spheres to solve problems. MAFS.912.G-MG.1.1 Use geometric shapes, their measures, and their properties to describe objects. MAFS.912.G-MG.1.3 Apply geometric methods to solve design problems.

This topic focuses on understanding, calculating and applying the surface area and volume of

spheres and hemispheres.

Section 14, Topic 9: Similar Shapes

MAFS.912.G-GMD.1.3 Use volume for cylinders, pyramids, cones, and spheres to solve problems. MAFS.912.G-SRT.1.2 Given two figures, use the definition of similarity transformations to decide if they are similar; explain using similarity

This topic explores the characteristics of similar solid and how to use those characteristics to find

lateral area, surface area, volume or missing segments.



transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.

Section 14, Topic 10: Cross Sections and Plane Rotations

MAFS.912.G-GMD.2.4 Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects. MAFS.912.G-MG.1.1 Use geometric shapes, their measures, and their properties to describe objects.

This topic focuses on visualizing the 2-dimensional cross-sections of prisms by removing

part of the solid. It also explores the plane rotations of 2-dimensional figures to form 3-

dimensional figures.



SECTION 15: ADDITIONAL MODELING WITH GEOMETRY

Section 15, Topic 1: Density

MAFS.912.G-MG.1.2 Apply concepts of density based on area and volume in modeling situations. MAFS.912.G-GMD.1.3 Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.

This topic focuses on how to apply concepts of density based on area and volume in real world

modeling situations.

Section 15, Topic 2: Minimizing and Maximizing

MAFS.912.G-MG.1.3 Apply geometric methods to solve design problems. MAFS.912.G-GMD.1.3 Use volume formulas for cylidners, pyramids, cones and spheres to solve problems. MAFS.912.G-MG.1.1 Use geometric shapes, their measures, and their properties to describe objects.

This topic focuses on how to apply geometric methods to real world modeling situation such as

minimizing cost or maximizing profit or area.

Section 15, Topic 3: Angles of Elevation and Depression

MAFS.912.G-SRT.3.6 Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles. MAFS.912.G-SRT.3.7 Explain and use the relationship between the sine and cosine of complementary angles. MAFS.912.G-SRT.3.8 Use trigonometric ratios and Pythagorean Theorem to solve right triangles in applied problems.

This topic discusses how to use trigonometric ratios and Pythagorean Theorem to solve right

triangles that are modeled or formed by angles of elevation and depression. Students learn how

to calculate angles, distance and height.

Section 15, Topic 4: Typographic Grid Systems Based on Ratios

MAFS.912.G-MG.1.3 Apply geometric methods to solve design problems. MAFS.912.G-GMD.1.3 Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.

This topic focuses on how to apply geometric methods to solve design problems when working

with typographic grid systems based on ratios.



MAFS.912.G-GPE.2.7 Use coordinates to computer perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula

Section 15, Topic 5: Areas in Real-World Contexts

MAFS.912.G-MG.1.1 Use geometric shapes, their measures, and their properties to describe objects. MAFS.912.G-MG.1.3 Apply geometric methods to solve design problems.

This topic applies the concept of 2-dimensional areas and 3-dimensional lateral and surface

areas to solve real world problems.

Section 15, Topic 6: Volume in Real-World Contexts

MAFS.912.G-MG.1.1 Use geometric shapes, their measures, and their properties to describe objects. MAFS.912.G-MG.1.3 Apply geometric methods to solve design problems. MAFS.912.G-GMD.1.3 Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.

This topic applies the concept of volume to solve real world problems.

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