Radnor High School - Radnor Township School District€¦ · Web viewThe perpendicular bisector of a segment The Perpendicular Bisector Theorem Concurrent lines Point of concurrency

Radnor High School Course Syllabus

Honors Geometry0428

Credits: 1 Grades: 9, 10Weighted: Yes Prerequisite: 8th Grade Algebra I with a "B" or Length: Year teacher recommendationFormat Meets daily

Overall Description of Course This course uses a disciplined approach to traditional Geometry, integrating the concepts and skills of the student's previous Algebra 1 course. Students in Honors Geometry apply geometric concepts to solve problems, use two-column proofs to establish relationships among triangles and parts of triangles, apply similarity theorems to geometric figures, relate knowledge of parallel and perpendicular lines to solve practical problems, combine algebraic and geometric skills to solve perimeter, area and volume problems, and apply skills involving trigonometry and transformational geometry.

Course Topics (Summary Outline)

Created 5/17/2011

I. Basic Ideas of Geometry Points, Lines, Planes, and Space Distance and Segment Measure Rays, Angles, and Angle Measure Congruent Segments and Angles Triangles Conditional Statements Drawing/Supporting Conclusions Deductive Reasoning Complementary, Supplementary, and Vertical

Angles Perpendicular Lines Diagram Rules Segment, Line, and Angle Theorems

II. Parallel Lines and Planes Parallel Planes, Lines, and Transversals Properties of Parallel Lines Proving Lines Parallel Angles of a Triangle Angle Sum Theorem for Triangles

III. Transformations Reflections and Line Symmetry Translations and Translational Symmetry Rotations and Rotational Symmetry

IV. Congruent Triangles Congruent Triangles Congruence Postulates Congruency Proofs Isosceles Triangles Medians, Altitudes, and Perpendicular Bisectors

V. Constructions Segments, Angles, and Bisectors Perpendicular and Parallel Lines

VI. Using Congruent Triangles and Parallel Lines Properties of Parallelograms Proving Quadrilaterals are Parallelogram Rectangles, Rhombuses, and Squares Trapezoids The Midsegment Theorem Inequalities in One Triangle

VII. Similarity Ratio and Proportion Properties of Proportion Similar Polygons AAS, SAS, and SSS Similarity Theorems Segments Divided Proportionally

VIII. Right Triangles Right Triangle Proportions The Pythagorean Theorem The Converse of the Pythagorean Theorem

Special Right Triangles The Tangent, Sine, and Cosine Ratios Angles of Elevation and Depression

Coordinate Geometry Midpoint of a Segment Slope of a Line Slopes of Perpendicular and Parallel Lines Equation of Lines The Distance Formula

Circles Basic Terms Tangent Lines Common Tangents and Tangent Circles Arcs and Chords Inscribed Angles Other Angles The Equations of a Circle

Area and Perimeter of Polygons Perimeter and Area of Rectangles Areas of Parallelogram and Triangles Areas of Trapezoids and Other Quadrilaterals Area of Regular Polygons Ratios of Areas and Perimeters of Similar

Polygons Circumference and Arc Lengths Areas of Circles, Sectors, and Segments

XII. Surface Area and Volume Prisms, Pyramids, Cylinders Cones, Spheres Similar Solid

Assignments & GradingAssignment sheets will be distributed periodically throughout the school year. Homework will be assigned on a daily basis. Grades will be based on quizzes and tests. In addition, teachers may use homework, group activities, and/or projects for grading purposes. All students will take departmental midyear and final exams. The Radnor High School grading system and scale will be used to determine letter grades.

Materials & Texts MATERIALS Graphing and/or scientific calculator; Compass and straight edge

TEXTS McDougal Littell, Larson et al, 2007

Media, Technology, Web Resourceshttp://www.classzone.com/cz/books/geometry_2007_na/book_home.htm?state=PA

FIRST MARKING PERIODUNIT: Reasoning and Proof

Keystone Connections:M11.E.1.1-Appropriately display and/or use data in problem-solving settings. (Reference: 2.6.11.A, 2.6.8.E)M11.A.2.1-Apply ratio and/or proportion in problem-solving situations. (Reference: 2.2.11.A, 2.8.11.P)M11.A.2.2-Use exponents, roots and/or absolute value to solve problems. (Reference: 2.1.11.A)M11.A.3.1-Apply the order of operations in computation and in problem-solving situations. (Reference: 2.2.8.A)M11.A.3.2-Use estimation strategies in problem-solving situations. (Reference: 2.2.11.B, 2.2.11.D)2.4.10.D-Use if . . . then, converse, inverse, and contra positive statements to construct simple valid arguments. 2.4.10.A-Use direct proofs, indirect proofs, or proof by contradiction to validate conjectures.2.4.10.C-Relate inductive and deductive reasoning to make observations about and to verify properties of figures. 2.1.10.A-Describe and apply inverse operations (reciprocal, absolute value, raising to power, finding roots and logarithms) to solve equations and inequalities.

Common Core Standards:

Student Objectives:Terminology:

Postulates for points, lines and planesDiagrams including points, lines and planesIdeas can and cannot be assumed from diagrams Algebraic properties of equalityDistributive propertyReflexive, symmetric and transitive properties

Student Objectives Write conditional statements in if-then form Write the converse, inverse and contrapositive of a conditional statementDetermine if the conditional statement is trueWrite biconditional statements for definitionsInterpret diagramsDetermine if certain idea can be assumed from a diagram

Use algebraic properties of equality to solve linear equationsUse distributive property in solving linear equationsIdentify reflexive, symmetric and transitive properties

Activities, Assignments, & AssessmentsACTIVITIES

Analyze Conditional Statements Use Postulates and Diagrams Reason Using Properties from Algebra

ASSIGNMENTS

Honors Geometry Chapters 1 & 2

#1: Identify Points, Lines and Planes (1.1)p. 5 – 8: # 3 – 11, 13 – 22, 25, 26, 40 – 42

#2: Use Segment & Congruence (1.2)

p. 12 – 14: # 6 – 11, 16 – 19, 21 – 25 odds, 27, 30

#3: Use Midpoint and Distance Formula (1.3) p. 19 – 22: # 2 – 8, 11 – 16, 17 – 21 odds, 26 – 30 evens, 31 – 34, 44, 57 – 59

#4: Measure and Classify Angles (1.4)

p. 28 – 32: # 3 – 14, 21 – 27, 29 – 31, 33 – 38, 40 – 42, 53

#5: Describe Angle Pair Relationships (1.5)p. 38 – 41: # 6 – 18 evens, 21 -27 odds, 31 – 38, 39 – 43 odds

#6: Review for Quiz

#7: Classify Polygons (1.6)p. 44 – 47: # 3 – 13, 15 – 23, 29, 40

#8: Find Perimeter, Circumference and Area (1.7)p. 52 – 56: # 4 – 14 evens, 17, 20 – 28 evens, 31, 33, 45

#9: Analyze Conditional Statements (2.2)p. 82 – 85: # 2 – 5, 7 – 15, 19 – 21, 25, 29, 41 – 45 odds

#10: Use Postulates and Diagrams (2.4)p. 99 – 102: # 3, 4, 5, 10, 11 – 13, 14 – 23, 24, 47 – 51 odds

#11: Reason Using Properties from Algebra (2.5)p. 108 – 111: # 3, 4, 21 – 26, 30 -32, 39, 40; Quiz 1 – 7

#12: Chapter Reviewp. 60 – 63: # 4 – 40 evens; p. 135 – 137: # 6 – 8, 12 – 16

#13: Algebra Reviewp. 139: # 1 – 23 odds

ASSESSMENTS

Quiz Section 1.1 – 1.5

Homework collection

Chapters 1 – 2 Test

Terminology

Conditional statementsThe hypothesisThe conclusionThe converseThe inverseThe contrapositiveEquivalent statememtsBiconditional statements

Media, Technology, Web Resourceshttp://www.classzone.com/cz/books/geometry_2007_na/book_home.htm?state=PA

Enduring Understandings

Essential QuestionsWhen should estimation be used as opposed to an exact answer in real life situations?

FIRST MARKING PERIODUNIT3: Parallel and Perpendicular Lines

Keystone Connections:M11.C.1.2-Recognize and/or apply properties of angles, triangles, and quadrilaterals. (Reference: 2.9.8.D, 2.9.11.C)2.9.10.B-Prove two triangles or two polygons are congruent or similar using algebraic and coordinate as well as deductive proofs.2.9.10.C-Identify and prove the properties of quadrilaterals involving opposite sides and angles, consecutive sides and angles, and diagonals using deductive proofs.2.9.10.D-Identify corresponding parts in congruent triangles to solve problems. M11.C.1.2-Recognize and/or apply properties of angles, triangles, and quadrilaterals. (Reference: 2.9.8.D, 2.9.11.C)2.1.10.A-Describe and apply inverse operations (reciprocal, absolute value, raising to power, finding roots and logarithms) to solve equations and inequalities.2.2.10.A-Develop and use computation concepts, operations and procedures on real numbers in problem solving situations. M11.C.1.2-Recognize and/or apply properties of angles, triangles, and quadrilaterals. (Reference: 2.9.8.D, 2.9.11.C)2.1.10.A-Describe and apply inverse operations (reciprocal, absolute value, raising to power, finding roots and logarithms) to solve equations and inequalities.2.2.10.A-Develop and use computation concepts, operations and procedures on real numbers in problem solving situations. M11.D.3.1-Describe and/or determine change. (Reference: 2.8.8.J, 2.11.8.B)M11.D.3.2-Compute and/or use the slope of a line. (Reference: 2.8.11.J, 2.8.11.L)2.2.10.A-Develop and use computation concepts, operations and procedures on real numbers in problem solving situations.2.2.10.C-Construct and apply mathematical models, including lines and curves of best fit, to estimate values of related quantities. M11.C.3.0-Geometry: Locate points or describe relationships using the coordinate plane.M11.C.3.1-Solve problems using analytic geometry. (Reference: 2.9.11.G)M11.D.2.1-Write, solve, and/or graph linear equations and inequalities using various methods. (Reference: 2.8.8.F; 2.8.11.D; 2.8.11.H; 2.8.11.J; 2.8.11.N; 2.8.11.L; 2.8.11.K)M11.D.3.1-Describe and/or determine change. (Reference: 2.8.8.J, 2.11.8.B)M11.D.3.2-Compute and/or use the slope of a line. (Reference: 2.8.11.J, 2.8.11.L)M11.D.4.1-Interpret and/or use linear, quadratic and/or exponential functions and their equations, graphs or tables. (Reference: 2.8.11.K, 2.8.11.Q,)2.1.10.A-Describe and apply inverse operations (reciprocal, absolute value, raising to power, finding roots and logarithms) to solve equations and inequalities. M11.B.2.1-Use and/or compare measurements of angles. (Reference: 2.3.11.a, 2.3.11.B)M11.C.3.1-Solve problems using analytic geometry. (Reference: 2.9.11.G)2.9.10.G-Solve problems using analytic geometry.2.9.10.I-Model situations geometrically to formulate and solve problems.

Common Core Standards

Student Objectives:Terminology:

Corresponding Angles PostulateTheorems for alternate interior/exterior angles and consecutive interior angles Corresponding Angles ConverseThe converses of the theorems for alternate interior/exterior angles and consecutive interior angles Slope of a line, including special lines (parallel and perpendicular)Equation of lines in Point-Slope, Slope-Intercept and General Linear forms y=m(x-h)+k; y=mx+b; Ax+By=C

Angles that are linear pairsRight angles at intersection of two linesAdjacent complementary anglesPerpendicular transversal theorem

Student Objectives

Determine if two lines are parallel or skewDetermine if two planes are parallelIdentify corresponding, alternate interior/exterior and consecutive interior angles Find the measures of corresponding, alternate interior/exterior and consecutive interior angles of two parallel lines Prove whether two lines are parallel given two angles Find the slope of a line from two pointsDetermine the slopes of parallel linesDetermine the slopes of perpendicular lines Write equation of a line in all three forms given two points or a point and the slopeWrite equations of parallel and perpendicular linesShow that two lines are perpendicular with congruent linear pair anglesShow that two lines are perpendicular with right angle formed at the intersectionShow that two lines are perpendicular with adjacent complementary anglesShow that two lines are parallel when they are perpendicular to the same line

Activities, Assignments, & AssessmentsACTIVITIES

Identify Pairs of Lines and Angles Use Parallel Lines and Transversals

Prove Lines are Parallel Find and Use Slopes of Lines Write and Graph Equations of Lines Prove Theorems about Perpendicular Lines

ASSIGNMENTS

Honors Geometry Chapters 3 - Parallel & Perpendicular Lines

#14: Identify Pairs of Lines and Angles (3.1)p. 150 – 152: # 3 – 6, 11 – 14, 16 – 32, 47

#15: Use Parallel Lines and Transversals (3.2)p. 157 – 160: # 3, 5 – 21 odds, 24, 27 – 35 odds

#16: Prove Lines are Parallel (3.3)p. 165 – 169: # 3 – 23 odds, 28

#17: Review for Quiz Worksheet

#18: Find and Use Slopes of Lines (3.4)p. 175 – 178: # 3 – 6, 13 – 29 odds, 30 – 32, 39 – 40

#19: Write & Graph Equations of Lines (3.5)p. 184 – 187: # 3 – 47 odds, 53 – 57 odds, 63

#20: Prove Theorems About Perpendicular Lines (3.6) p. 193 – 197: # 2 – 10, 13 – 21 odds, 39 – 47 odds

#21: Chapter Reviewp. 202 – 205: # 3 – 26

ASSESSMENTS

Homework collection, Chapter 3 Quiz, Chapter 3 Test

TerminologyParallel linesSkew linesParallel planes

Perpendicular linesTransversalCorresponding, alternate interior/exterior, consecutive interior angles

FIRST MARKING PERIODUNIT4: CONGRUENT TRIANGLES

Keystone Connections: M11.C.1.2-Recognize and/or apply properties of angles, triangles, and quadrilaterals. (Reference: 2.9.8.D, 2.9.11.C)M11.C.1.3-Use properties of congruence, correspondence and similarity in problem-solving settings involving two- and three-dimensional figures. (Reference: 2.9.11.B)2.9.10.B-Prove two triangles or two polygons are congruent or similar using algebraic and coordinate as well as deductive proofs.2.9.10.D-Identify corresponding parts in congruent triangles to solve problems.2.9.10.J-Analyze figures in terms of the kinds of symmetries they have. M11.C.1.2-Recognize and/or apply properties of angles, triangles, and quadrilaterals. (Reference: 2.9.8.D, 2.9.11.C)M11.C.1.3-Use properties of congruence, correspondence and similarity in problem-solving settings involving two- and three-dimensional figures. (Reference: 2.9.11.B)2.4.10.A-Use direct proofs, indirect proofs, or proof by contradiction to validate conjectures.2.4.10.C-Relate inductive and deductive reasoning to make observations about and to verify properties of figures.2.9.10.B-Prove two triangles or two polygons are congruent or similar using algebraic and coordinate as well as deductive proofs. M11.C.1.2-Recognize and/or apply properties of angles, triangles, and quadrilaterals. (Reference: 2.9.8.D, 2.9.11.C)M11.C.1.3-Use properties of congruence, correspondence and similarity in problem-solving settings involving two- and three-dimensional figures. (Reference: 2.9.11.B)2.4.10.A-Use direct proofs, indirect proofs, or proof by contradiction to validate conjectures.2.4.10.C-Relate inductive and deductive reasoning to make observations about and to verify properties of figures.2.9.10.B-Prove two triangles or two polygons are congruent or similar using algebraic and coordinate as well as deductive proofs. M11.C.1.3-Use properties of congruence, correspondence and similarity in problem-solving settings involving two- and three-dimensional figures. (Reference: 2.9.11.B)M11.C.1.2-Recognize and/or apply properties of angles, triangles, and quadrilaterals. (Reference: 2.9.8.D, 2.9.11.C)2.4.10.A-Use direct proofs, indirect proofs, or proof by contradiction to validate conjectures.2.4.10.C-Relate inductive and deductive reasoning to make observations about and to verify properties of figures.2.9.10.B-Prove two triangles or two polygons are congruent or similar using algebraic and coordinate as well as deductive proofs. M11.C.1.2-Recognize and/or apply properties of angles, triangles, and quadrilaterals. (Reference: 2.9.8.D, 2.9.11.C)M11.C.1.3-Use properties of congruence, correspondence and similarity in problem-solving settings involving two- and three-dimensional figures. (Reference: 2.9.11.B)2.1.10.A-Describe and apply inverse operations (reciprocal, absolute value, raising to power, finding roots and logarithms) to solve equations and inequalities.2.2.10.A-Develop and use computation concepts, operations and procedures on real numbers in problem solving situations.

2.4.10.A-Use direct proofs, indirect proofs, or proof by contradiction to validate conjectures.2.9.10.B-Prove two triangles or two polygons are congruent or similar using algebraic and coordinate as well as deductive proofs.2.9.10.C-Identify and prove the properties of quadrilaterals involving opposite sides and angles, consecutive sides and angles, and diagonals using deductive proofs.


TERMINOLOGY:KNOWLEDGE Types of trianglesacute,right,obtuse,equiangularscalene,isosceles,equilateral

Interior/exterior angles of a triangleTriangle Sum TheoremExterior Angle Theorem Congruent figuresCorresponding partsThird Angle TheoremProperties of congruent trianglesConguence statement Side-Side-Side Congruence PostulateTwo-column proof Side-Angle-Side Congruence PostulateHypotenuse-Leg Congruence Theorem Angle-Side-Angle Congruence PostulateAngle-Angle-Side Congruence Theorem CPCTCCommon Segment TheoremCommon Angle Theorem Isosceles trianglesThe vertex of an isosceles triangleThe legs of an isosceles triangleThe base of an isosceles triangleBase anglesThe altitude from the vertex of an isosceles triangleEquilateral triangles

STUDENT OBJECTIVES: Identify the type of a triangle base on sides and anglesUse the Triangle Sum Theorem to find the measures of angles in a triangleUse the Exterior Angle Theorem to find measures of angles of a triangle Identify corresponding parts of congruent figures

Use congurences to find measure/length of corresponding partsApply the Third Angle TheoremWrite congruence statement for two congruent polygons Prove two triangles congruent by SSSWrite two-column proofs Prove two triangles congruent by SASProve two right triangles congruent by HL Prove two triangles congruent by ASAProve two triangles congruent by AAS Use congruent triangles to prove that corresponding parts are congruentUse the Common Segement/Common Angle Theorem in the proof of congruent triangles Use the properties of an isosceles triangle to find the lengths of sides and measures of angles in an isosceles triangleUse the property of the altitude from the vertex of an isosceles triangle



Activities, Assignments, & AssessmentsACTIVITIESApply Triangle Sum Properties Apply Congruence and Triangles Prove Triangles Congruent by SSS Prove Triangles Congruent by SAS and HL Prove Triangles Congruent by ASA and AAS Use Congruent Triangles Use Isosceles and Equilateral Triangles

ASSIGNMENTS

Chapter 4 – Congruent TrianglesDon't forget to draw sketches, show your work, and jot down questions!

#22: Applying Triangle Sum Properties (4.1) p. 221 – 224: # 1 – 6, 11 – 19 odds, 21 – 27, 31 – 37 odds, 44 – 47

#23: Apply Congruence and Triangles (4.2) p. 228 – 231: # 3 – 16, 19 – 21

#24: Prove Triangles Congruent by SSS (4.3)

p. 236 – 239: # 1 – 7, 11, 16 – 19, 21, 34 – 36

#25: Prove Triangles Congruent by SAS & HL (4.4)p. 243 – 246: # 3 – 19 odds, 20 – 22, 25, 27, 30, 39


#27: Prove Triangles Congruent by ASA & AAS (4.5)p. 252 – 255: # 3 – 5, 7 – 10, 12, 14 – 20, 37 – 43 odds

#28: Use Congruent Triangles (4.6)p. 259 – 263: # 3 – 9, 13 – 20, 27, 28, 31, 33 – 35

#29: Isosceles & Equilateral Triangles (4.7) p. 267 – 270: # 3 – 29 odds, 32 – 33, 46 – 48

#30: Chapter Reviewp. 282 – 285: #1 – 26

ASSESSMENTS Chapter 4 quiz; Chapter 4 test; homework collection

2nd Marking PeriodUnit: Chapter 4 Proofs

Students will continue with the concepts presented in chapter four to complete two column proofs. They will be responsible for turning

in several homework assignments as well as completing a quiz at the end of the unit.

Unit 5: Relationships within Triangles

Keystone Connections:M11.C.1.2-Recognize and/or apply properties of angles, triangles, and quadrilaterals. (Reference: 2.9.8.D, 2.9.11.C)2.1.10.A-Describe and apply inverse operations (reciprocal, absolute value, raising to power, finding roots and logarithms) to solve equations and inequalities.2.2.10.A-Develop and use computation concepts, operations and procedures on real numbers in problem solving situations.2.4.10.A-Use direct proofs, indirect proofs, or proof by contradiction to validate conjectures. M11.C.1.2-Recognize and/or apply properties of angles, triangles, and quadrilaterals. (Reference: 2.9.8.D, 2.9.11.C)2.1.10.A-Describe and apply inverse operations (reciprocal, absolute value, raising to power, finding roots and logarithms) to solve equations and inequalities.2.2.10.A-Develop and use computation concepts, operations and procedures on real numbers in problem solving situations.2.4.10.A-Use direct proofs, indirect proofs, or proof by contradiction to validate conjectures.2.9.10.B-Prove two triangles or two polygons are congruent or similar using algebraic and coordinate as well as deductive proofs.2.9.10.C-Identify and prove the properties of quadrilaterals involving opposite sides and angles, consecutive sides and angles, and diagonals using deductive proofs. M11.C.1.2-Recognize and/or apply properties of angles, triangles, and quadrilaterals. (Reference: 2.9.8.D, 2.9.11.C)2.1.10.A-Describe and apply inverse operations (reciprocal, absolute value, raising to power, finding roots and logarithms) to solve equations and inequalities.2.2.10.A-Develop and use computation concepts, operations and procedures on real numbers in problem solving situations.2.4.10.A-Use direct proofs, indirect proofs, or proof by contradiction to validate conjectures.2.4.10.B-Constructs algorithms for multi-step and real world problems.2.9.10.B-Prove two triangles or two polygons are congruent or similar using algebraic and coordinate as well as deductive proofs.2.9.10.C-Identify and prove the properties of quadrilaterals involving opposite sides and angles, consecutive sides and angles, and diagonals using deductive proofs. M11.C.1.2-Recognize and/or apply properties of angles, triangles, and quadrilaterals. (Reference: 2.9.8.D, 2.9.11.C)2.1.10.A-Describe and apply inverse operations (reciprocal, absolute value, raising to power, finding roots and logarithms) to solve equations and inequalities.2.2.10.A-Develop and use computation concepts, operations and procedures on real numbers in problem solving situations.2.4.10.A-Use direct proofs, indirect proofs, or proof by contradiction to validate conjectures.

2.4.10.B-Constructs algorithms for multi-step and real world problems.


TerminologyKNOWLEDGE Midsegment of a triangleMidsegment TheoremCoordinate proof The perpendicular bisector of a segmentThe Perpendicular Bisector TheoremConcurrent linesPoint of concurrencyThe circumcenter of a trianglePythagorean Theorem Angle bisectorAngle Bisector TheoremThe incenter of a triangle Medians of a triangleThe centroid of a triangleThe orthocenter of a triangle Triangle Inequality TheoremRelationship between side lengths and angle measures in a triangleThe Hinge Theorem

Student Objectives: Use the Midsegment Theorem to find the lengths and angle measures in a triangleUse the coordinate proof in certain proving problems Determine if a point is on the perpendicular bisector of a segmentDetermine if a point is equidistant from the endpoints of a segmentLocate the circumcenter by drawing the perpendicular bisectorsUse the property of the circumcenter and the Pythagorean Theorem to find the missing length Determine if a ray is the bisector of an angleDetermine if a point is on the bisector of an angleLocate the incenter by drawing the angle bisectors Use the property of the incenter and the Pythagorean Theorem to find missing lengths in a triangle Locate the centroid by drawing the medians of a triangleUse the property of the centroid to find the missing lengths in a triangleLocate the orthocenter by drawing the altitudes of a triangle Determine the longest/shortest side in a triangleDetermine the largest/smallest angle in a triangleDetermine the possible length of one side given the other two side lengthsDetermine if the given side lengths form a triangle

use the hinge theorem to determine the relative measures of sides and angles



Activities, Assignments, & AssessmentsACTIVITIESMidsegment Theorem and Coordinate Proof Use Perpendicular Bisectors Use Angle Bisectors of Triangles Use Medians and Altitudes Use Inequalities in a Triangle

ASSIGNMENTS

Chapter 5: Relationship With Triangles#36: Midsegment Theorem (5.1)

p. 298 – 301 # 3 – 11, 24 – 26, 28, 31, 39, 47 – 51 odds

#37: Use Perpendicular Bisector (5.2)p. 306 – 309: # 3 – 17, 20 – 22, 34 – 38

#38: Use Angle Bisectors of Triangles (5.3) p. 313 – 316: #3 – 25 odds, 28, 29, 39 – 45 odds


#40: Use Medians & Altitudes (5.4)p. 322 – 325: # 3 – 8, 13 – 27 odds, 33 – 35, 36, 41, 47, 49

#41: Use Inequalities in a Triangle (5.5)p. 331 – 334: # 6 – 12, 16 – 26 evens, 31, 33, 35, 36

#42: Chapter Reviewp. 346 – 347: # 3 – 24

ASSESSMENTS homework collection, quiz, test

Unit 6: Similarity

Keystone Connections:M11.A.2.1-Apply ratio and/or proportion in problem-solving situations. (Reference: 2.2.11.A, 2.8.11.P)M11.C.1.2-Recognize and/or apply properties of angles, triangles, and quadrilaterals. (Reference: 2.9.8.D, 2.9.11.C)M11.C.1.3-Use properties of congruence, correspondence and similarity in problem-solving settings involving two- and three-dimensional figures. (Reference: 2.9.11.B)2.2.10.A-Develop and use computation concepts, operations and procedures on real numbers in problem solving situations. M11.A.2.1-Apply ratio and/or proportion in problem-solving situations. (Reference: 2.2.11.A, 2.8.11.P)2.2.10.A-Develop and use computation concepts, operations and procedures on real numbers in problem solving situations.M11.C.1.2-Recognize and/or apply properties of angles, triangles, and quadrilaterals. (Reference: 2.9.8.D, 2.9.11.C)M11.C.1.3-Use properties of congruence, correspondence and similarity in problem-solving settings involving two- and three-dimensional figures. (Reference: 2.9.11.B) M11.A.2.1-Apply ratio and/or proportion in problem-solving situations. (Reference: 2.2.11.A, 2.8.11.P)M11.C.1.2-Recognize and/or apply properties of angles, triangles, and quadrilaterals. (Reference: 2.9.8.D, 2.9.11.C)M11.C.1.3-Use properties of congruence, correspondence and similarity in problem-solving settings involving two- and three-dimensional figures. (Reference: 2.9.11.B)2.1.10.A-Describe and apply inverse operations (reciprocal, absolute value, raising to power, finding roots and logarithms) to solve equations and inequalities.2.2.10.A-Develop and use computation concepts, operations and procedures on real numbers in problem solving situations.2.4.10.A-Use direct proofs, indirect proofs, or proof by contradiction to validate conjectures.2.9.10.B-Prove two triangles or two polygons are congruent or similar using algebraic and coordinate as well as deductive proofs. M11.C.1.2-Recognize and/or apply properties of angles, triangles, and quadrilaterals. (Reference: 2.9.8.D, 2.9.11.C)M11.C.1.3-Use properties of congruence, correspondence and similarity in problem-solving settings involving two- and three-dimensional figures. (Reference: 2.9.11.B)M11.A.2.1-Apply ratio and/or proportion in problem-solving situations. (Reference: 2.2.11.A, 2.8.11.P)2.1.10.A-Describe and apply inverse operations (reciprocal, absolute value, raising to power, finding roots and logarithms) to solve equations and inequalities.2.2.10.A-Develop and use computation concepts, operations and procedures on real numbers in problem solving situations.2.4.10.A-Use direct proofs, indirect proofs, or proof by contradiction to validate conjectures.2.9.10.B-Prove two triangles or two polygons are congruent or similar using algebraic and coordinate as well as deductive proofs. M11.A.2.1-Apply ratio and/or proportion in problem-solving situations. (Reference: 2.2.11.A, 2.8.11.P)M11.C.1.2-Recognize and/or apply properties of angles, triangles, and quadrilaterals.

(Reference: 2.9.8.D, 2.9.11.C)M11.C.1.3-Use properties of congruence, correspondence and similarity in problem-solving settings involving two- and three-dimensional figures. (Reference: 2.9.11.B)2.1.10.A-Describe and apply inverse operations (reciprocal, absolute value, raising to power, finding roots and logarithms) to solve equations and inequalities.2.2.10.A-Develop and use computation concepts, operations and procedures on real numbers in problem solving situations.2.4.10.A-Use direct proofs, indirect proofs, or proof by contradiction to validate conjectures.2.9.10.B-Prove two triangles or two polygons are congruent or similar using algebraic and coordinate as well as deductive proofs. M11.A.2.1-Apply ratio and/or proportion in problem-solving situations. (Reference: 2.2.11.A, 2.8.11.P)M11.C.1.2-Recognize and/or apply properties of angles, triangles, and quadrilaterals. (Reference: 2.9.8.D, 2.9.11.C)M11.C.1.3-Use properties of congruence, correspondence and similarity in problem-solving settings involving two- and three-dimensional figures. (Reference: 2.9.11.B)2.1.10.A-Describe and apply inverse operations (reciprocal, absolute value, raising to power, finding roots and logarithms) to solve equations and inequalities.2.2.10.A-Develop and use computation concepts, operations and procedures on real numbers in problem solving situations.2.4.10.A-Use direct proofs, indirect proofs, or proof by contradiction to validate conjectures.2.9.10.B-Prove two triangles or two polygons are congruent or similar using algebraic and coordinate as well as deductive proofs.


Terminology:KNOWLEDGE Ratiosproportionsgeometric meanExtremes and means of a proprotionProperty of proportions Different ways to write equivalent proportionsScaleSimilar polygonsCorresponding angles of similar polygonsCorresponding sides of similar polygonsScale factorPerimeters of similar polygonsCorresponding lengthsSimilarity statement Angle-Angle Similarity Postulate Side-Side-Side Similarity TheoremSide-Angle-Side Similarity Theorem

Triangle Proportionality TheoremRelationship of side lengths in a triangle with an angle bisectorRelationship of lengths on two transversal cut by three parallel lines

STUDENT OBJECTIVES: SKILLS Simplify ratiosUse ratios to find lengths or angle measuresSolve proportionsFind the geometric mean of two numbers Write equivalent proportions of a given proportionUse the scale to find lengths Write similarity statement for similar polygonsIdentify congruent angles and proportional side lengthsDetermine if two polygons are similarFind the scale factor of the two similar polygonsUse similarity to find the perimeters of similar polygonsUse similarity to find the corresponding lengths Prove two triangles similar by AA Prove two triangles similar by SSSProve two triangles similar by SAS Use the Triangle Proportionality Theorem to find the lengths in a triangleFind the missing length in a triangle with an angle bisectorFind the missing length when three parallel lines cut two transversal

Materials & Texts

MATERIALS Graphing and/or scientific calculator; Compass and straight edge


Activities, Assignments, & AssessmentsACTIVITIESRatios, Proportions, and the Geometric Mean Use Proportions to Solve Geometry Problems Use Similar Polygons Prove Triangles Similar by AA Prove Triangles Similar by SSS and SAS Use Proportionality Theorems

ASSIGNMENTSChapter 6: Similarity

Draw sketches and show your work to earn full credit!!

#43: Ratios, Proportions & the Geometric Mean (6.1)p. 360 – 363: # 3 – 45 odds, 49 – 57 odds, 68, 71

#44: Use Proportions to Solve Geometry Problems (6.2) p. 367 – 370: # 3 – 12, 16 – 18, 22, 24, 29,

#45: Use Similar Polygons (6.3)p. 376 – 379: # 3 – 12, 14 – 17, 19 – 21, 23 – 26, 28, 34, 41 – 47 odds


#47: Prove Triangles are Similar by AA (6.4)p. 384 -387: # 3 – 17, 20, 21, 26 – 32, 41 – 45

#48: Prove Triangles are Similar by SSS & SAS (6.5) p. 391 – 395: #3 – 12, 14, 21 – 23, 25, 26, 33, 38, 43, 44

#49: Use Proportionality Theorems (6.6) p. 400 - 402 # 3 – 7 odds, 8, 9 – 17 odds, 24

#50: Chapter Review

p. 418 – 421: # 4 – 18

#51: Algebra Reviewp. 423: #1 – 17 odds

ASSESSMENTS 2 quizzes; 1 test; homework collection

3rd Marking PeriodUnit 7: Right Triangles and Trigonometry

Keystone Connections:M11.C.1.2-Recognize and/or apply properties of angles, triangles, and quadrilaterals. (Reference: 2.9.8.D, 2.9.11.C)M11.C.1.4-Solve problems involving right triangles using the Pythagorean Theorem. (Reference: 2.10.11.B)M11.A.3.1-Apply the order of operations in computation and in problem-solving situations. (Reference: 2.2.8.A)2.1.10.A-Describe and apply inverse operations (reciprocal, absolute value, raising to power, finding roots and logarithms) to solve equations and inequalities. M11.C.1.2-Recognize and/or apply properties of angles, triangles, and quadrilaterals. (Reference: 2.9.8.D, 2.9.11.C)M11.C.1.4-Solve problems involving right triangles using the Pythagorean Theorem. (Reference: 2.10.11.B)2.1.10.A-Describe and apply inverse operations (reciprocal, absolute value, raising to power, finding roots and logarithms) to solve equations and inequalities. M11.C.1.2-Recognize and/or apply properties of angles, triangles, and quadrilaterals. (Reference: 2.9.8.D, 2.9.11.C)M11.C.1.3-Use properties of congruence, correspondence and similarity in problem-solving settings involving two- and three-dimensional figures. (Reference: 2.9.11.B)2.1.10.A-Describe and apply inverse operations (reciprocal, absolute value, raising to power, finding roots and logarithms) to solve equations and inequalities.2.9.10.B-Prove two triangles or two polygons are congruent or similar using algebraic and coordinate as well as deductive proofs. M11.C.1.2-Recognize and/or apply properties of angles, triangles, and quadrilaterals. (Reference: 2.9.8.D, 2.9.11.C)2.10.10.B-Express trigonometric ratios as fractions or decimals and describe their relationships to right triangles.2.1.10.A-Describe and apply inverse operations (reciprocal, absolute value, raising to power, finding roots and logarithms) to solve equations and inequalities. 2.10.10.B-Express trigonometric ratios as fractions or decimals and describe their relationships to right triangles.M11.A.2.1-Apply ratio and/or proportion in problem-solving situations. (Reference: 2.2.11.A, 2.8.11.P)M11.C.1.2-Recognize and/or apply properties of angles, triangles, and quadrilaterals. (Reference: 2.9.8.D, 2.9.11.C)2.1.10.A-Describe and apply inverse operations (reciprocal, absolute value, raising to power, finding roots and logarithms) to solve equations and inequalities. M11.C.1.2-Recognize and/or apply properties of angles, triangles, and quadrilaterals. (Reference: 2.9.8.D, 2.9.11.C)2.1.10.A-Describe and apply inverse operations (reciprocal, absolute value, raising to power, finding roots and logarithms) to solve equations and inequalities.2.3.10.C-Represent the relationship among linear dimension, area, and volume and the corresponding uses of units, square units, and cubic units of measure using physical models.2.3.10.D-Create and write and solve real world problems that involve the concepts of absolute and relative errors in measurements.

2.10.10.B-Express trigonometric ratios as fractions or decimals and describe their relationships to right triangles. M11.C.1.2-Recognize and/or apply properties of angles, triangles, and quadrilaterals. (Reference: 2.9.8.D, 2.9.11.C)2.10.10.B-Express trigonometric ratios as fractions or decimals and describe their relationships to right triangles.2.1.10.A-Describe and apply inverse operations (reciprocal, absolute value, raising to power, finding roots and logarithms) to solve equations and inequalities.


Terminology:KNOWLEDGE Pythagorean TheoremPythagorean triplesThe Converse of the Pythagorean Theorem Similar right trianglesGeometric means in right triangle with altitude drawn to the hypotenuse (HLLS & SAAS) 45°-45°-90° triangle30°-60°-90° triangle Right triangle trigonometric ratioTangent ratio Sine ratioCosine ratioAngle of elevation/depressionApply the sine or cosine ratio to find the missing length of a leg or the hypotenuse of a right triangle Use angle of elevation/depression to find lengths/distance in real life problems Inverse trigonometric ratiosInverse tangent ratioInverse sine ratioInverse cosine ratio

STUDENT OBJECTIVES:Use the Pythagorean Theorem to find the missing side length of a right triangle, the height and slant height of a pyramidUtilize the Pythgorean triples to find the missing length quicklyUse the Pythagorean Theorem to find the lengths of the diagonal of a rectangular boxClassify triangles as acute, obtuse or right based on their side lengthsSolve quadratic inequalities Write proportionality statement for similar right trianglesUse the geometric means to find the missing side lengths in a right triangle with altitude drawn to the hypotenuse Use the properties of 45°-45°-90° triangle to find the missing side lengthsUse the properties of 30°-60°-90° triangle to find the missing side lengths Apply the tangent ratio to find the missing length of a leg of a right triangle

Solve a right triangle by finding all side lengths and angle measures



Activities, Assignments, & AssessmentsACTIVITIESApply the Pythagorean Theorem Use the Converse of the Pythagorean Theorem Use Similar Right Triangles Special Right Triangles Apply the Tangent Ratio Apply the Sine and Cosine Ratios Solve Right Triangles

ASSIGNMENTS

Chapter 7: Right Triangles & TrigonometryDraw sketches and show your work to earn full credit!!

#52: Applying Pythagorean Theorem (7.1)p. 436 – 439: # 3 – 27 odds, 28 – 30, 35, 39 – 49 odds

#53: Use the Converse of the Pythagorean Theorem (7.2)p. 444- 447: #3 – 33 odds, 34, 43, 49 – 52

#54: Use Similar Right Triangles (7.3)p. 453 – 456: # 3 – 29 odds, 39 – 49 odds

#55: Special Right Triangles (7.4)p. 461 – 464: # 4 – 10 evens, 11, 12, 13 – 27 odds, 34, 35 – 38, 39 – 43 odds


#57: Right Triangle Worksheet with 3D applications

#58: Apply the Tangent Ratio (7.5)p. 469 – 472: #3 – 29 odds, 30 – 32, 38, 41 – 47 odds

#59: Apply the Sine and Cosine Ratios (7.6)p. 477 – 480: # 3 – 15 odds, 18, 19 – 31 odds, 33, 35, 36

#60: Solve Right Triangles (7.7)p. 485 – 489: # 3 – 29 odds, 33, 38

#61: Chapter Reviewp. 494 – 497: # 5 – 33 odds

#62: Algebra Review: Solving Quadratic Equationsp. 499: #7 – 17 odds

ASSESSMENTS : 2 quizzes, test, homework collection

3rd Marking PeriodUnit 8 : Quadrilaterals

Keystone Connections:M11.C.1.2-Recognize and/or apply properties of angles, triangles, and quadrilaterals. (Reference: 2.9.8.D, 2.9.11.C)2.1.10.A-Describe and apply inverse operations (reciprocal, absolute value, raising to power, finding roots and logarithms) to solve equations and inequalities.2.2.10.A-Develop and use computation concepts, operations and procedures on real numbers in problem solving situations. M11.C.1.2-Recognize and/or apply properties of angles, triangles, and quadrilaterals. (Reference: 2.9.8.D, 2.9.11.C)2.1.10.A-Describe and apply inverse operations (reciprocal, absolute value, raising to power, finding roots and logarithms) to solve equations and inequalities.2.2.10.A-Develop and use computation concepts, operations and procedures on real numbers in problem solving situations.2.4.10.B-Constructs algorithms for multi-step and real world problems.2.5.10.C-Construct algorithms for solving multistep and non-routine real world problems.2.9.10.D-Identify corresponding parts in congruent triangles to solve problems.2.9.10.B-Prove two triangles or two polygons are congruent or similar using algebraic and coordinate as well as deductive proofs.2.9.10.C-Identify and prove the properties of quadrilaterals involving opposite sides and angles, consecutive sides and angles, and diagonals using deductive proofs.2.4.10.A-Use direct proofs, indirect proofs, or proof by contradiction to validate conjectures. M11.C.1.2-Recognize and/or apply properties of angles, triangles, and quadrilaterals. (Reference: 2.9.8.D, 2.9.11.C)2.1.10.A-Describe and apply inverse operations (reciprocal, absolute value, raising to power, finding roots and logarithms) to solve equations and inequalities.2.2.10.A-Develop and use computation concepts, operations and procedures on real numbers in problem solving situations.2.4.10.B-Constructs algorithms for multi-step and real world problems.2.5.10.C-Construct algorithms for solving multistep and non-routine real world problems.2.9.10.D-Identify corresponding parts in congruent triangles to solve problems.2.9.10.B-Prove two triangles or two polygons are congruent or similar using algebraic and coordinate as well as deductive proofs.2.9.10.C-Identify and prove the properties of quadrilaterals involving opposite sides and angles, consecutive sides and angles, and diagonals using deductive proofs.2.4.10.A-Use direct proofs, indirect proofs, or proof by contradiction to validate conjectures. M11.C.1.2-Recognize and/or apply properties of angles, triangles, and quadrilaterals. (Reference: 2.9.8.D, 2.9.11.C)2.1.10.A-Describe and apply inverse operations (reciprocal, absolute value, raising to power, finding roots and logarithms) to solve equations and inequalities.2.2.10.A-Develop and use computation concepts, operations and procedures on real numbers in problem solving situations.2.4.10.B-Constructs algorithms for multi-step and real world problems.2.9.10.B-Prove two triangles or two polygons are congruent or similar using algebraic and

coordinate as well as deductive proofs.2.9.10.C-Identify and prove the properties of quadrilaterals involving opposite sides and angles, consecutive sides and angles, and diagonals using deductive proofs.2.9.10.D-Identify corresponding parts in congruent triangles to solve problems.2.4.10.A-Use direct proofs, indirect proofs, or proof by contradiction to validate conjectures. M11.C.1.2-Recognize and/or apply properties of angles, triangles, and quadrilaterals. (Reference: 2.9.8.D, 2.9.11.C)2.1.10.A-Describe and apply inverse operations (reciprocal, absolute value, raising to power, finding roots and logarithms) to solve equations and inequalities.2.2.10.A-Develop and use computation concepts, operations and procedures on real numbers in problem solving situations.2.4.10.B-Constructs algorithms for multi-step and real world problems.2.9.10.B-Prove two triangles or two polygons are congruent or similar using algebraic and coordinate as well as deductive proofs.2.9.10.C-Identify and prove the properties of quadrilaterals involving opposite sides and angles, consecutive sides and angles, and diagonals using deductive proofs.2.9.10.D-Identify corresponding parts in congruent triangles to solve problems.2.4.10.A-Use direct proofs, indirect proofs, or proof by contradiction to validate conjectures. M11.C.1.2-Recognize and/or apply properties of angles, triangles, and quadrilaterals. (Reference: 2.9.8.D, 2.9.11.C)2.9.10.C-Identify and prove the properties of quadrilaterals involving opposite sides and angles, consecutive sides and angles, and diagonals using deductive proofs.


Terminology:KNOWLEDGE Diagonals of a polygonInterior angles of a polygon(n-2)180

Exterior angles of a polygon-sum is 360 degrees parallelogram-a quadrilateral with both pairs of opposite sides parallel

Properties of a parallelogram-opposite sides are congruent-opposite angles are congruent-consecutive angles are supplementary-diagonals bisect each other The converses of the theorems regarding the properties of a parallelogram

Rhombuses and their propertiesRectangles and their propertiesSquare and their properties Trapezoids and their propertiesIsosceles trapezoids and their propertiesMidsegment of a trapezoid and its propertiesKites and their properties Special quadrilaterals

Student Objectives: Find the sum of the measures of all interior angles of a polygonFind the measure of the missing angle in a polygonFind the measure of an exterior angle of polygonFind the measure of an interior angle of a regular polygon Determine the number of sides a regular polygon Use the properties of a parallelogram to find the side lengths or angle measures Identify parallelograms as rhombues, rectangles or squaresUse the properties of rhombuses, rectangles and squares to find the missing lengths and angle measures Prove that a quadrilateral is a trapezoid or an isosceles trapezoidUse the properties of isosceles trapezoids to find missing side lengths and angle measuresProve that a quadrilaeral is a kiteUse the properties of kites to find missing side lengths and angle measures Identify special quadrilaterals



Activities, Assignments, & AssessmentsACTIVITIESFind Angle Measures in Polygons Use Properties of Parallelograms Show that a Quadrilateral is a Parallelogram Properties of Rhombuses, Rectangles, and Squares Use Properties of Trapezoids and Kites Identify Special Quadrilaterals

ASSIGNMENTS Chapter 9: Properties of Transformation

#71: Translate Figures (9.1) p. 576 – 579: # 3 – 14, 30, 47 – 53 odds

#72: Perform Reflections (9.3)p. 593 – 596: # 3 – 11 odds, 12, 23, 27, 28

#73: Perform Rotations (9.4) p. 602 – 605: # 3 – 8, 12 – 14, 20, 21, 23, 41 – 45 odds

#74: Chapter Review Worksheet


ASSESSMENTS: Homework collection, quiz

Unit 9: TRANSFORMATIONS

Keystone Connections:M11.C.3.1-Solve problems using analytic geometry. (Reference: 2.9.11.G)2.9.10.G-Solve problems using analytic geometry.2.1.10.A-Describe and apply inverse operations (reciprocal, absolute value, raising to power, finding roots and logarithms) to solve equations and inequalities.2.2.10.A-Develop and use computation concepts, operations and procedures on real numbers in problem solving situations.2.9.10.H-Construct a geometric figure and its image using various transformations. M11.C.3.1-Solve problems using analytic geometry. (Reference: 2.9.11.G)2.9.10.J-Analyze figures in terms of the kinds of symmetries they have.2.9.10.G-Solve problems using analytic geometry. M11.C.3.1-Solve problems using analytic geometry. (Reference: 2.9.11.G)2.9.10.J-Analyze figures in terms of the kinds of symmetries they have.2.9.10.H-Construct a geometric figure and its image using various transformations.


Student Objectives:Terminology Transformations Preimage Image Translation Isometry Reflection Line of reflection Rules for reflections in the coordinate plane Lines of reflectional symmetry Rotation Angles of rotations Angles of rotational symmetry

Student Objectives Perform the translation to find the image of the preimage Find the preiamge of an image under a translationPerform reflection of figures over any line Perform reflection of figures over x-axis, y-axis, line y = x and line y = -x Determine the number of lines of reflectional symmetry for certain figures Perform rotations of a figure about a point through an angle Perform rotations of a figure about the origin through 90°, 180° and 270°

Determine all angles of rotational symmetry for regular polygons



Activities, Assignments, & AssessmentsACTIVITIESTranslate Figures Perform Reflections Perform Rotations

ASSIGNMENTS

Chapter 9: Properties of Transformation#71: Translate Figures (9.1)

p. 576 – 579: # 3 – 14, 30, 47 – 53 odds #72: Perform Reflections (9.3)

p. 593 – 596: # 3 – 11 odds, 12, 23, 27, 28

#73: Perform Rotations (9.4) p. 602 – 605: # 3 – 8, 12 – 14, 20, 21, 23, 41 – 45 odds

#74: Chapter Review Worksheet


ASSESSMENTSQuiz, test, homework collection

4th Marking PeriodUnit 10: Properties of Circles

Keystone Connections:M11.C.1.1-Identify and/or use parts of circles and segments associated with circles. (Reference: 2.9.11.F)2.9.10.F-Use the properties of angles, arcs, chords, tangents, and secants to solve problems involving circles.2.4.10.A-Use direct proofs, indirect proofs, or proof by contradiction to validate conjectures.2.9.10.B-Prove two triangles or two polygons are congruent or similar using algebraic and coordinate as well as deductive proofs.2.1.10.A-Describe and apply inverse operations (reciprocal, absolute value, raising to power, finding roots and logarithms) to solve equations and inequalities. M11.C.1.1-Identify and/or use parts of circles and segments associated with circles. (Reference: 2.9.11.F)2.9.10.F-Use the properties of angles, arcs, chords, tangents, and secants to solve problems involving circles.2.1.10.A-Describe and apply inverse operations (reciprocal, absolute value, raising to power, finding roots and logarithms) to solve equations and inequalities.2.3.10.C-Represent the relationship among linear dimension, area, and volume and the corresponding uses of units, square units, and cubic units of measure using physical models. M11.C.1.1-Identify and/or use parts of circles and segments associated with circles. (Reference: 2.9.11.F)2.9.10.F-Use the properties of angles, arcs, chords, tangents, and secants to solve problems involving circles.2.1.10.A-Describe and apply inverse operations (reciprocal, absolute value, raising to power, finding roots and logarithms) to solve equations and inequalities. M11.C.1.1-Identify and/or use parts of circles and segments associated with circles. (Reference: 2.9.11.F)2.9.10.F-Use the properties of angles, arcs, chords, tangents, and secants to solve problems involving circles.2.1.10.A-Describe and apply inverse operations (reciprocal, absolute value, raising to power, finding roots and logarithms) to solve equations and inequalities.

M11.A.3.2-Use estimation strategies in problem-solving situations. (Reference: 2.2.11.B, 2.2.11.D)M11.C.1.1-Identify and/or use parts of circles and segments associated with circles. (Reference: 2.9.11.F)2.9.10.F-Use the properties of angles, arcs, chords, tangents, and secants to solve problems involving circles.2.1.10.A-Describe and apply inverse operations (reciprocal, absolute value, raising to power, finding roots and logarithms) to solve equations and inequalities. M11.C.3.1-Solve problems using analytic geometry. (Reference: 2.9.11.G)2.1.10.A-Describe and apply inverse operations (reciprocal, absolute value, raising to power, finding roots and logarithms) to solve equations and inequalities.2.4.10.B-Constructs algorithms for multi-step and real world problems.

2.8.10.E-Graph equations representing, conic sections (e.g., circles, ellipses, parabolas and hyperbolas.)


Terminology CircleCenter of a circleRadius & diameterChords, tangents and secantsPoint of tangencyRelationship of a tangent and the radius at the point of tangencyTangent segments from a common external pointCommon internal/external tangentsInternal/external tangent circlesConcentric circles Central angleArcMinor & major arcsArc measuresCongruent circles/arcs Congruent chordsProperties of chords in a circleProperties of congruent chords Inscribed anglesIntercepted arcInscribed/circumscribed polygons/circlesRelationship of angles in an inscribed quadrilateral Tangent-chord angleAngle formed at the intersection of two chordsAngle formed at the intersection of two tangentsAngle formed at the intersection of a tangent and a secantAngle formed at the intersection of two secants outside the circlechord-chord power theoremtangent-secant power theoremsecant-secant power theorem Standard equation of a circle

Student Objectives: Find the radius and diameter of a circleName a circleDetermine if circles are internal/external tangent or concentric circlesUse the property of a tangent and the radius at the point of tangency

Use the property of the tangent segments from a common externalpointFind the length of the common external tangent segment of two circles Find the arc measuresDetermine if an arc is minor or majorDetermine if two arcs are congruent Determine if two chords are congruentUse the relationship of a chord and a diameter perpendicular to it to find missing lenghtsUse the properties of congruent chords to find lengths and distance from the chords to the center Find the measures of inscribed anglesDetermine the angle measures of an inscribed quadrilateral Find the measure of a tangent-chord angleFind the measure of the angle formed at the intersection of two chordsFind the measure of the angle formed at the intersection of two tangents, two secants or a tangent and a secantfind the lengths of circle segments using the power theoremsWrite the standard equation of a circle given the endpoints of a diameter or three points on the circleDraw a circle on the coordinate plane



Activities, Assignments, & AssessmentsACTIVITIESUse Properties of Tangents Find Arc Measures Apply Properties of Chords Use Inscribed Angles and Polygons Apply Other Angle Relationships in Circles Write and Graph Equations

ASSIGNMENTSChapter 10: Properties of Circles

Draw sketches and show your work to earn full credit!!

#76: Use Properties of Tangents (10.1)p. 655 – 658: # 3 – 10, 12 – 17, 18 – 26 evens, 29, 30, 34, 42, 43 – 47 odds

#77: Find Arc Measures (10.2)p. 661 – 663: # 3 – 14, 17 – 20, 27 – 33 odds

#78: Apply Properties of Chords (10.3)p. 667 – 670: # 3 – 11 odds, 12 – 15, 18 – 20, 29, 35


#80: Use Inscribed Angles and Polygons (10.4) p. 676 – 679: # 3 – 15 odds, 16 – 18, 20 – 25, 40 – 46 evens

#81: Apply Other Angle Relationships in Circles (10.5)p. 683 – 686: # 3 – 6, 7 – 13 odds, 16 – 18, 20 – 23, 35 – 39 odds

#82: Write and Graph Equations of Circles (10.7)p. 702 – 705: # 3 – 25 odds, 26, 31, 33, 49 – 53 odds

#83: Chapter Reviewp. 708 – 711: # 4 – 22, 25 – 31 odds

ASSESSMENTS2 Quizzes , homework collection, test

Unit 11 Measuring Length and Area


Keystone Connections:

Terminology: Bases of a parallelogram height of a parallelogram height of a trapezoidCircumference arc length sector of a circle

Center of a polygon radius of a polygon apothem of a polygonCentral angle of a regular polygon

probability

Student Objectives: The students will use area formulas for polygons.Relate length, perimeter, and area ratios in similar polygonsCompare measures for parts of circles and the whole circle.



Assignments: Chapter 11: Measuring Length and Area

Draw sketches and show your work to earn full credit! Write the formula for each problem.

#84: Area s of Triangles and Parallelograms (11.1)p. 723 – 726: # 3 – 8, 13 – 19 odds, 23 – 27 odds, 30, 33, 36, 37, 48 - 50

#85: Area of Trapezoids, Rhombuses, and Kites (11.2)p. 733 – 736: # 3 – 15 odds, 16 – 18, 22, 25 – 29 odds, 31, 32, 47, 48

#86: Area of Regular Polygons (11.6)p. 765 – 768: # 1 – 4, 6 – 16, 18, 19 – 27 odds, 31 – 33, 35, 36


#88: Perimeter and Area of Similar Figures (11.3)p. 740 – 743: # 3 – 15 odds, 17, 19, 20, 22, 23, 25, 27, 35 – 41 odds

#89: Circumference & Arc Length (11.4)p. 749 – 752: # 3 – 27 odds, 32, 36, 42 – 45

#90: Area of Circle & Sectors (11.5)p. 758 – 781: # 3 – 31 odds, 36, 45 – 51 odds

Assessments:

Quiz, homework collection, test

Chapter 12 Surface Area and Volume of Solids


Keystone Connections:

Terminology: Polyhedron net cone face edge

vertexRight prism right cone oblique prism volume

cylinderSphere prism right cylinder

great circle surface areaPyramid hemisphere lateral area regular pyramid

similar solids

Student Objectives:Exploring Solids and their propertiesSolving problems using surface area and volumeConnecting similarity to solids



Assignments:Chapter 12: Surface Area & Volume of Solids

Draw sketches and show your work to earn full credit! Write the formula for each problem.

#92: Surface Area of Prisms & Cylinders (12.2)p. 806 – 809: # 3 – 8, 10 – 16 even, 17 – 23 odd, 31 – 37 odd

#93: Surface Area of Pyramids and Cones (12.3)

p. 814 – 817: # 3 – 23 odd, 26, 31, 34, 35 – 39 odd, Quiz # 2 – 7 all

#94: Volume of Prisms & Cylinders (12.4)p. 823 – 825: # 3 – 23 odd, 27, 34 – 40 even

# 95: Review for Quiz Worksheet

#96: Volumes of Pyramids & Cones (12.5)p. 832 – 836: # 4 – 24 even, 28, 30 – 32, 36, 43 – 51 odds

#97: Surface Area & Volume of Spheres (12.6)p. 842 – 845: # 3 – 9 odd, 10 – 28 even, 30, 33, 40 – 44 all

#98: Explore Similar Solids (12.7)p. 850 – 854: # 3 – 23 odd, 30, 32, 37 – 47 odd

#99: Chapter Reviewp. 858 – 860: # 6 – 22

Assessments: 2 quizzes, 1 test, homework collection

Documents

Radnor High School - Radnor Township School District€¦ · Web viewThe perpendicular bisector of a segment The Perpendicular Bisector Theorem Concurrent lines Point of concurrency