Math:Geometry Term:1 · base angles of isosceles triangles, midsegments, and medians, and apply these relationships to solve problems 7.1 Interior and Exterior Angles 1 G.6(D) Supporting

Math:Geometry Term: 1The student uses mathematical processes to acquire and demonstrate mathematical understanding.

Transformations and Congruence

Days TEKS Student Expectation Resources Textbook

1 G.2(A)Supporting

determine the coordinates of a point that is a given fractional distance less than one from one end of a line segment to the other in one- and two-dimensional coordinate systems, including finding the midpoint

1.1 Segment Length and Midpoints

TI-Nspire: Points, Lines, & Distance

2 G.5(B)Supporting

construct congruent segments, congruent angles, a segment bisector, an angle bisector, perpendicular lines, the perpendicular bisector of a line segment, and a line parallel to a given line through a point not on a line using a compass and a straightedge

1.2 Angle Measures and Angle Bisectors

construct angles using protractor

2 G.3(A)Supporting

describe and perform transformations of figures in a plane using coordinate notation

1.3 Representing and Describing Transformations

2 G.4(C)Readiness

verify that a conjecture is false using a counterexample 1.4 Reasoning and Proof

G.4(A)Supporting

distinguish between undefined terms, definitions, postulates, conjectures, and theorems

1.4 Reasoning and Proof

2 G.4(B)Supporting

identify and determine the validity of the converse, inverse, and contrapositive of a conditional statement and recognize the connection between a biconditional statement and a true conditional statement with a true converse

1.5 Related Conditionals

1 G.3(A)Supporting


2.1 Translations

1 G.3(A)Supporting


2.2 Reflections

Wednesday, June 08, 2016 Page 1 of 13Revised Date:

Transformations and Congruence


2 G.3(B)Readiness

determine the image or pre-image of a given two-dimensional figure under a composition of rigid transformations, a composition of non-rigid transformations, and a composition of both, including dilations where the center can be any point in the plane

2.3 RotationsNspire: Reflections & Rotations

1 G.3(D)Supporting

identify and distinguish between reflectional and rotational symmetry in a plane figure

2.4 Investigating Symmetry

1 G.3(C)Supporting

identify the sequence of transformations that will carry a given pre-image onto an image on and off the coordinate plane

3.1 Sequences of Transformations

2 G.6(C)Supporting

apply the definition of congruence, in terms of rigid transformations, to identify congruent figures and their corresponding sides and angles

3.2 Proving Figures are Congruent Using Rigid Motions

1 G.6(C)Supporting


3.3 Corresponding Parts of Congruent Figures are Congruent

Lines, Angles, and Triangles


1 G.6(A)Readiness

verify theorems about angles formed by the intersection of lines and line segments, including vertical angles, and angles formed by parallel lines cut by a transversal and apply these relationships to solve problems

4.1 Angles Formed by Intersecting Lines

1 G.5(A)Readiness

investigate patterns to make conjectures about geometric relationships, including angles formed by parallel lines cut by a transversal choosing from a variety of tools

4.2 Transversals and Parallel Lines

Nspire: Creating parallel lines and transversal




1 G.6(A)Readiness

prove equidistance between the endpoints of a segment and points on its perpendicular bisector and apply these relationships to solve problems

4.3 Proving Lines are Parallel

2 G.5(B)Supporting


4.4 Perpendicular Lines

2 G.2(C)Readiness

determine an equation of a line parallel or perpendicular to a given line that passes through a given point

4.5 Equations of Parallel and Perpendicular Lines

1 G.6(C)Supporting


5.1 Exploring what makes Triangles Congruent

1 G.6(B)Readiness

prove two triangles are congruent by applying the Side-Angle-Side, Angle-Side-Angle, Side-Side-Side, Angle-Angle-Side, and Hypotenuse-Leg congruence conditions

5.2 ASA Triangle Congruence

1 G.6(B)Readiness


5.3 SAS Triangle Congruence

1 G.5(C)Supporting

use the constructions of congruent segments, congruent angles, angle bisectors, and perpendicular bisectors to make conjectures about geometric relationships

5.4 SSS Triangle Congruence

Nspire: SSA: The Ambiguous Case





1 G.6(B)Supporting


6.2 AAS Triangle Congruence

1 G.6(B)Readiness


6.3 HL Triangle Congruence

1 G.6(D)Supporting

verify theorems about the relationships in triangles, including proof of the Pythagorean Theorem, the sum of interior angles, base angles of isosceles triangles, midsegments, and medians, and apply these relationships to solve problems

7.1 Interior and Exterior Angles

1 G.6(D)Supporting


7.2 Isosceles and Equilateral Triangles

1 G.5(D)Supporting

verify the Triangle Inequality theorem using constructions and apply the theorem to solve problems

7.3 Triangle Inequalities

Nspire: Triangle Inequality Thm.

G.6(D)Supporting


1 G.5(A)Readiness

investigate patterns to make conjectures about geometric relationships, including angles formed by parallel lines cut by a transversal choosing from a variety of tools

8.1 Perpendicular Bisectors of Triangles - circumcenter

patty paper activity




1 G.5(A)Readiness

investigate patterns to make conjectures about geometric relationships, including special segments of triangles choosing from a variety of tools

8.2 Angle Bisectors of Triangles - incenter

2 G.6(D)Supporting


8.3 Medians and Altitudes of Triangles

Nspire: Special Segments in Triangles

1 G.6(D)Supporting


8.4 Midsegments of Triangles

Quadrilaterals and Coordinate Proof


1 G.5(A)Readiness

investigate patterns to make conjectures about geometric relationships, including interior and exterior angles of polygons choosing from a variety of tools

9.1 Properties of Parallelograms

1 G.6(E)Supporting

prove a quadrilateral is a parallelogram, rectangle, square, or rhombus using opposite sides,opposite angles, or diagonals and apply these relationships to solve problems.

9.2 Conditions for Parallelograms

1 G.6(E)Supporting

prove a quadrilateral is a parallelogram, rectangle, square, or rhombus using opposite sides,opposite angles, or diagonals and apply these relationships to solve problems.

9.3 Properties of Rectangles, Rhombuses, and Squares

1 G.5(A)Readiness

investigate patterns to make conjectures about geometric relationships, including interior and exterior angles of polygons choosing from a variety of tools

9.4 Conditions for Rectangles, Rhombuses, and Squares




2 G.5(A)Readiness

investigate patterns to make conjectures about geometric relationships including criteria required for triangle congruence choosing from a variety of tools

9.5 Properties and Conditions for Kites and Trapezoids





1 G.2(B)Readiness

derive and use the distance, slope, and midpoint formulas to verify geometric relationships, including congruence of segments and parallelism or perpendicularity of pairs of lines

10.1 Slope and Parallel Lines

1 G.2(B)Readiness


10.2 Slope and Perpendiuclar Lines

1 G.2(B)Readiness


10.3 Coordinate Proof Using Distance with Segments and Triangles

1 G.6(E)Supporting

prove a quadrilateral is a parallelogram, rectangle, square, or rhombus using opposite sides, opposite angles, or diagonals and apply these relationships to solve problems

10.4 Coordinate Proof using Distance with Quadrilaterals

2 G.11(B)Readiness

determine the area of composite two-dimensional figures comprised of a combination of triangles, parallelograms, trapezoids, kites, regular polygons, or sectors of circles to solve problems using appropriate units of measure

10.5 Perimeter and Area on the Coordinate

Similarity


1 G.3(C)Supporting

identify the sequence of transformations that will carry a given pre-image onto an image on and off the coordinate plane

11.1 Dilations


Similarity


1 G.7(A)Supporting

apply the definition of similarity in terms of a dilation to identify similar figures and their proportional sides and the congruent corresponding angles

11.2 Proving Figures are Similar Using Transformations

1 G.7(A)Supporting

apply the definition of similarity in terms of a dilation to identify similar figures and their proportional sides and the congruent corresponding angles

11.3 Corresponding Parts of Similar Figures

1 G.7(B)Readiness

apply the Angle-Angle criterion to verify similar triangles and apply the proportionality of the corresponding sides to solve problems

11.4 AA Similarity of Triangles

1 G.8(A)Supporting

prove theorems about similar triangles, including the Triangle Proportionality theorem, and apply these theorems to solve problems

12.1 Triangle Proportionality Theorem

1 G.2(A) 12.2 Subdividing a segment in a given ratio

1 G.8(A)Supporting

prove theorems about similar triangles, including the Triangle Proportionality theorem, and apply these theorems to solve problems

12.3 Using Proportional Relationships

1 G.8(B)Supporting

identify and apply the relationships that exist when an altitude is drawn to the hypotenuse of a right triangle, including the geometric mean, to solve problems

12.4 Similarity in Right Triangles

Trigonometry


1 G.9(A)Readiness

determine the lengths of sides and measures of angles in a right triangle by applying the trigonometric ratios sine, cosine, and tangent to solve problems

13.1 Tangent Ratio


Trigonometry


2 G.9(A)Readiness


13.2 Sine and Cosine Ratio

2 G.9(B)Readiness

apply the relationships in special right triangles 30°-60°-90° and 45°-45°-90° and the Pythagorean theorem, including Pythagorean triples, to solve problems

13.3 Special Right Triangles

2 G.9(A)Readiness


13.4 Problem solving with Trig

Properties of Circles


2 G.5(A)Readiness

Investigate patterns to make conjectures about geometric relationships, including angles formed by parallel lines cut by a transversal choosing from a variety of tools

14.1 Central Angles and Inscribed Angles

1 G.12(A)Supporting

apply theorems about circles, including relationships among angles, radii, chords, tangents, and secants, to solve non-contextual problems

14.2 Angles in Inscribed Quadrilaterals

2 G.5(A)Readiness

investigate patterns to make conjectures about geometric relationships, including special segments and angles of circles choosing from a variety of tools

14.3 Tangents and Circumscribed Angles

1 G.12(A)Supporting


14.4 Segment Relationships in Circles

1 G.12(A)Supporting


14.5 Angle Relationships in Circles

1 G.10(B)Readiness

determine and describe how changes in the linear dimensions of a shape affect its perimeter, area, surface area, or volume, including proportional and non-proportional dimensional change

15.1 Justifying Circumference and Area of a Circle


Properties of Circles


1 G.12(D)Supporting

describe radian measure of an angle as the ratio of the length of an arc intercepted by a central angle and the radius of the circle

15.2 Arc Length and Radian Measure

1 G.12(C)Supporting

apply the proportional relationship between the measure of the area of a sector of a circle and the area of the circle to solve problems

15.3 Sector Area

1 G.12(E)Supporting

show that the equation of a circle with center at the origin and radius r is x2 + y2 = r2 and determine the equation for the graph of a circle with radius r and center (h, k), (x – h)2 + (y – k)2 = r2.

15.4 Equation of a Circle



Measurement & Modeling in 2 & 3 Dimensions


1 G.11(D)Readiness

apply the formulas for the volume of three-dimensional figures, including prisms, pyramids, cones, cylinders, spheres, and composite figures, to solve problems using appropriate units of measure

16.1 Volume of Prisms and Cylinders

1 G.11(D)Readiness


16.2 Volume of Pyramids

1 G.11(D)Readiness


16.3 Volume of Cones

1 G.11(D)Readiness


16.4 Volume of Spheres

1 G.10(A)Supporting

identify the shapes of two-dimensional cross-sections of prisms, pyramids, cylinders, cones, and spheres and identify three-dimensional objects generated by rotations of two-dimensional shapes

17.1 Cross-Sections and Solids of Rotation

1 G.11(C)Readiness

apply the formulas for the total and lateral surface area of three-dimensional figures, including prisms, pyramids, cones, cylinders, spheres, and composite figures, to solve problems using appropriate units of measure

17.2 Surface Area of Prisms and Cylinders

1 G.11(C)Readiness


17.3 Surface Area of Pyramids and Cones


Measurement & Modeling in 2 & 3 Dimensions


1 G.11(C)Readiness


17.4 Surface Area of Spheres

2 G.11(B)Readiness

determine the area of composite two-dimensional figures comprised of a combination of triangles, parallelograms, trapezoids, kites, regular polygons, or sectors of circles to solve problems using appropriate units of measure

18.1 Perimeter and Area in Problem Solving

1 G.13(B)Supporting

determine probabilities based on area to solve contextual problems

18.2 Geometric Probability

1 G.11(A)Supporting

apply the formula for the area of regular polygons to solve problems using appropriate units of measure

18.4 Regular Polygons

2 G.4(D)Supporting

compare geometric relationships between Euclidea and spherical geometries, including parallel lines and the sum of the angles in a triangle

18.5 Modeling Geometry on a Spere

Probability


1 G.13(C)Readiness

identify whether two events are independent and compute the probability of the two events occurring together with or without replacement

19.1 Probability and Set Theory

2 G.13(A)Supporting

develop strategies to use permutations and combinations to solve contextual problems

19.3 Combinations and Probability

2 G.13(A)Supporting

develop strategies to use permutations and combinations to solve contextual problems

19.2 Permutations and Probability


Probability


1 G.13(C)Readiness


19.4 Mutually Exclusive and Overlapping Events

1 G.13(D)Supporting

apply conditional probability in contextual problems 20.1 Conditional Probability

1 G.13(C)Readiness


20.2 Independent Events

1 G.13(E)Supporting

apply independence in contextual problems 20.3 Dependent Events


Documents

Math:Geometry Term:1 · base angles of isosceles triangles, midsegments, and medians, and apply these relationships to solve problems 7.1 Interior and Exterior Angles 1 G.6(D) Supporting