public schools - uw-milwaukee

Mathematics Pacing Guide: High School Geometry Course

Math_Pacing Guide Geometry_07.27.11_v1 Page | 1 This Pacing Guide is to be used in conjunction with the Curriculum Guide and the Instructional Design Lesson Plan. The Curriculum Guide addresses the specific standards, essential understandings, misconceptions, instructional practices, and differentiation. The Instructional Design will help with planning lessons using Launch-Explore-Summarize-Apply.

Mathematics Curriculum Guide

High School Geometry

MILWAUKEE

PUBLIC SCHOOLS



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Common Core State Standards For Mathematics

Program Materials Discovering Geometry

Formative Assessments

Summative Assessments

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Domain: Congruence G-CO Cluster: Experiment with transformations in the plane Standard: 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. Domain: Geometric Measurement and Dimension G-MD Cluster: Visualize relationships between two-dimensional and three-dimensional objects Standard: 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.

Chapter 1: Introducing Geometry Lesson 1.1: Building Blocks of Geometry Investigation: Mathematical Models

Lesson 1.2: Poolroom Math Investigation: Virtual Pool

Lesson 1.3: What’s a Widget? Investigation: Defining Angles

Lesson 1.4: Polygons Investigation: Special Polygons

Lesson 1.5: Triangles Investigation: Triangles

Lesson 1.6: Special Quadrilaterals Investigation: Special Quadrilaterals

Lesson 1.7: Circles Investigation: Defining Circle Terms

Lesson 1.8: Space Geometry Investigation: Space Geometry Lesson 1.9: A Picture is Worth a Thousand Words Using Your Algebra Skills Midpoint Possible Extension Exploration: Geometric Probability I

Marzano’s Building Academic Vocabulary: Have students create a word wall including terms, descriptions, and visual representations to refer back to throughout the course. Use strategies such as: Talk-A-Mile-A-Minute Charades Pictionary Graphic Organizers I Have, Who Has

Quiz Chapter 1 Test: Introducing Geometry More Projects and Explorations: Key Curriculum Resources



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Domain: Congruence G-CO Cluster: Prove geometric theorems Standard: 9. Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints.

Chapter 2: Reasoning in Geometry Lesson 2.1: Inductive Reasoning Investigation: Shape Shifters

Lesson 2.2: Finding the nth Term Investigation: Finding the Rule

Lesson 2.3: Mathematical Modeling Investigation: Party Handshakes

Lesson 2.4: Deductive Reasoning Investigation: Overlapping Segments

Lesson 2.5: Angle Relationships Investigation 1: The Linear Pair Conjecture Investigation 2: Vertical Angles Conjecture

Lesson 2.6: Special Angles on Parallel Lines Investigation1: Which Angles are Congruent? Investigation 2: Is the Converse True?

Using Your Algebra Skills: Slope Possible Extension Explorations: The Seven Bridges of Konigsberg Patterns in Fractals

CABS: Parallel Lines Sally’s Doorbell Mary’s Dots

Quiz Chapter 2 Test: Reasoning in Geometry Chapter 2 More Projects and Explorations: Key Curriculum Resources



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Domain: Congruence G-CO Cluster: Understand congruence in terms of rigid motions Standards: 6. Use geometric descriptions of rigid motions to transform figures and to predict the effect of a rigid motion on a figure 7. Explain using rigid motions the meaning of congruence for triangles as the equality of all corresponding pairs of sides and all corresponding pairs of angles. 8. Explain how the criteria for triangle congruence follow from the definition of congruence.

Cluster: Prove geometric theorems Standard: 9. Prove theorems about lines and angles.

Cluster: Make geometric constructions Standard: 12. Make formal geometric constructions with a variety of tools and methods 13. Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.

Domain: Circles G-C Cluster: Understand and apply theorems about circles Standard: 3. Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.

Domain: Expressing Geometric Properties with Equations G-GPE Cluster: Use coordinates to prove simple geometric theorems algebraically Standard: 5. Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems

Chapter 3: Using Tools of Geometry

Lesson 3.1: Duplicating Segments and Angles Investigation1: Duplicating a Segment Investigation 2: Duplicating an Angle

Lesson 3.2: Constructing Perpendicular Bisectors Investigation1:Finding the Right Bisector Investigation 2: Constructing the Perpendicular Bisector

Lesson 3.3: Constructing Perpendiculars to a Line Investigation1:Finding the Right Line Investigation2: Patty-Paper Perpendiculars

Lesson 3.4: Constructing Angle Bisectors Investigation1:Angle Bisecting by Folding Investigation 2: Angle Bisecting with Compass

Lesson 3.5: Constructing Parallel Lines Investigation: Constructing Parallel Lines by Folding

Lesson 3.6: Construction Problems

Lesson 3.7: Constructing Points of Concurrency Investigation1: Concurrence Investigation2: Circumcenter Investigation 3: Incenter

Lesson 3.8: The Centroid Investigation1: Are medians Concurrent? Investigation2: Balancing Act

Using Your Algebra Skills: Slope of Parallel and Perpendicular Lines

Possible Extension Explorations: Perspective Drawing The Euler Line

CABS: Perpendicular Bisector Sketch It! Project: Is There More to the Orthocenter?( p. 192)

Quiz Chapter 3 Test: Using Tools of Geometry Chapter 3 More Projects and Explorations: Key Curriculum Resources



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Domain: Congruence G-CO Cluster: Understand congruence in terms of rigid motions Standard: 8. Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.

Cluster: Prove geometric theorems Standard: 10. Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.

Domain: Similarity, Right Triangles, and Trigonometry G-SRT Cluster: Prove theorems involving similarity Standard: 5. Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

Chapter 4: Discovering and Proving Triangle Properties

Lesson 4.1: Triangle Sum Conjecture Investigation1: The Triangle Sum

Lesson 4.2: Properties of Isosceles Triangles Investigation1:Base Angles in an Isosceles Triangle Investigation 2: Is the Converse True?

Lesson 4.3: Triangle Inequalities Investigation1: What is the Shortest Path from A to B? Investigation2: Where Are the Largest and Smallest Angles? Investigation 3: Exterior Angles of a Triangle

Lesson 4.4: Are There Congruence Shortcuts? Investigation1: Is SSS a Congruence Shortcut? Investigation 2: Is SAS a Congruence Shortcut? Investigation 3: IS SSA a Congruence Shortcut?

Lesson 4.5: Are There Other Congruence Shortcuts? Investigation1: Is ASA a Congruence Shortcut? Investigation2: Is SAA a Congruence Shortcut? Investigation3: Is AAA a Congruence Shortcut?

Lesson 4.6: Corresponding Parts of Congruent Triangles

Lesson 4.7: Flowchart Thinking

Lesson 4.8: Proving Special Triangle Conjectures Investigation: The Symmetry Line in an Isosceles Triangle

Using Your Algebra Skills: Solving Equations

Possible Extension Explorations: Napoleon’s Theorem

CABS: Triangle PBJ Projects: Polya’s Problem (p.236) or Lines and Isosceles Triangles (p.250)

Quiz Chapter 4 Test: Discovering and Proving Triangle Properties Chapter 4 More Projects and Explorations: Key Curriculum Resources



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Domain: Congruence G-CO Cluster: Prove geometric theorems Standards: 10. Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.

11. Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals.

Domain: Modeling with Geometry G-MG Cluster: Apply geometric concepts in modeling situations Standard: 3. Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).

Chapter 5: Discovering and Proving Polygon Properties

Lesson 5.1: Polygon Sum Conjecture Investigation: Is there a Polygon Sum Formula?

Lesson 5.2: Exterior Angles of a Polygon Investigation: Is There an Exterior Angle Sum?

Lesson 5.3: Kite and Trapezoid Properties Investigation1: What are Some Properties of Kites? Investigation2: What are Some Properties of Trapezoids?

Lesson 5.4: Properties of Midsegments Investigation1: Triangle Midsegment Properties Investigation 2: Trapezoid Midsegment Properties

Lesson 5.5: Properties of Parallelograms Investigation: Four Parallelogram Properties

Lesson 5.6: Properties of Special Parallelograms Invest1: What Can You Draw with the Double-Edged Straightedge? Invest2: Do Rhombus Diagonals Have Special Properties? Invest3: Do Rectangle Diagonals Have Special Properties?

Lesson 5.7: Proving Quadrilateral Properties Investigation: Finding the Square Root

Using Your Algebra Skills: Writing Linear Equations

Possible Extension Explorations: Star Polygon

Projects: Building an Arch (p.280) and Japanese Puzzle Quilts (p. 303) *These projects are needed to address the modeling standard.

Quiz Chapter 5 Test: Discovering and Proving Polygon Properties Chapter 5 More Projects and Explorations: Key Curriculum Resources



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Domain: Circles G-C Cluster: Understand and apply theorems about circles Standards: 2. Identify and describe relationships among inscribed angles, radii, and chords. 3. Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle. 4. (+) Construct a tangent line from a point outside a given circle to the circle.

Cluster: Find arc lengths and areas of sectors of circles Standard: 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.

Domain: Geometric Measurement and Dimension G-GMD Cluster: Explain volume formulas and use them to solve problems Standard: 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.

Domain: Modeling with Geometry G-MG Cluster: Apply geometric concepts in modeling situations Standard: 3. Apply geometric methods to solve design problems

Chapters 6: Discovering and Proving Circle Properties

Lesson 6.1: Tangent Properties Investigation1:Going Off on a Tangent Investigation2: Tangent Segments

Lesson 6.2: Chord Properties Investigation1:Defining Angles in a Circle Investigation2: Chords and Their Central Angles Investigation3: Chords and the Center of the Circle Investigation4: Perpendicular Bisector of a Chord

Lesson 6.3: Arcs and Angles Investigation1: Inscribed Angle Properties Investigation2: Inscribed Angles Intercepting the Same Arc Investigation3: Angles Inscribed in a Semicircle Investigation4: Cyclic Quadrilaterals Investigation5: Arcs by Parallel Lines

Lesson 6.4: Proving Circle Conjectures

Lesson 6.5: The Circumference/Diameter Ratio Investigation: A Taste of Pi

Lesson 6.6: Around the World

Lesson 6.7: Arc Length Investigation: Finding the Arcs

Using Your Algebra Skills: Solving Systems of Linear Equations

Possible Extension Explorations: Intersecting Lines Through a Circle

Project: Racetrack Geometry (p.354) * This project is needed to address the modeling standard. Have students apply the definitions and properties of circles to solve problems

Have students communicate logical arguments to show the truth of theorems pertaining to circles and explain clearly why the reasoning is valid

Quiz Chapter 6 Test: Discovering and Proving Circle Properties Chapter 6 More Projects and Explorations: Key Curriculum Resources



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Chapters 1 – 6 Review Semester 1 District Final Exam



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Domain: Congruence G-CO Cluster: Experiment with transformations in the plane Standards: 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 (e.g., translation versus horizontal stretch).

3. Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.

4. Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.

5. Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.

Cluster: Understand congruence in terms of rigid motions Standard: 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.


Chapter 7: Transformations and Tessellations Lesson 7.1: Transformations and Symmetry Investigation: The Basic Property of Reflection

Lesson 7.2: Properties of Isometries Investigation1:Transformations on a Coordinate Plane Investigation2: Finding a Minimal Path

Lesson 7.3: Compositions of Transformations Investigation1: Reflections across Two Parallel Lines Investigation2: Reflections across Two Intersecting Lines

Using Your Algebra Skills Finding Points of Concurrency

Possible Extension Exploration and Lessons: Tessellating with Conway Criterion

Lesson 7.4: Tessellations with Regular Polygons Investigation: The Semiregular Tessellations

Lesson 7.5: Tessellations with Nonregular Polygons Investigation1: Do All Triangles Tessellate? Investigation2: Do All Quadrilaterals Tessellate?

Lesson 7.6: Tessellations Using Only Translations

Lesson 7.7: Tessellations That Use Rotations

CABS: Reflect This! My Initials Project: Kaleidoscopes (p.402) * This project is needed to address the modeling standard. Students should be able to recognize and perform transformations using various geometric tools (i.e. patty paper, graph paper, etc.)

Students should be able to determine and define which rigid motion will move one given congruent figure to another

Quiz Chapter 7 Test: Transformations and Tessellations Chapter 7 More Projects and Explorations: Key Curriculum Resources



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Domain: Circles G-C Cluster: Find arc lengths and areas of sectors of circles Standard: 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.

Domain: Geometric Measure and Dimension G-GMD Cluster: Explain volume formulas and use them to solve problems Standard: 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.

Chapter 8: Area Lesson 8.1: Areas of Rectangles and Parallelograms Investigation: Area Formula for Parallelograms

Lesson 8.2: Areas of Triangles, Trapezoids and Kites Investigation1:Area Formula for Triangles Investigation2: Area Formula for Trapezoids Investigation3: Area Formula for Kites

Lesson 8.3: Area Problems Investigation: Solving Problems with Area Formulas

Lesson 8.4: Area of Regular Polygons Investigation: Area Formula for Regular Polygons

Lesson 8.5: Areas of Circles Investigation: Area Formula for Circles

Lesson 8.6: Any Way You Slice It

Lesson 8.7: Surface Area Investigation1: Surface Area of a Regular Pyramid Investigation2: Surface Area of a Cone

Using Your Algebra Skills Products, Factors, and Quadratic Equations

Possible Extension Explorations: Pick’s Formula for Area Geometric Probability II Alternative Area Formulas

CABS: Tommy’s Deck Project: Maximizing Area (p. 433)

Quiz Chapter 8 Test: Area Chapter 8 More Projects and Explorations: Key Curriculum Resources



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Domain: Expressing Geometric Properties with Equation G-GPE Cluster: Translate between the geometric description and the equation for a conic section Standard: 1. Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.

Cluster: Use coordinates to prove simple geometric theorems algebraically Standard: 7. Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.*

Chapter 9: Pythagorean Theorem Lesson 9.1: The Theorem of Pythagoras Investigation: The Three Sides of a Right Triangle

Lesson 9.2: The Converse of the Pythagorean Theorem Investigation: Is the Converse True?

Lesson 9.3: Two Special Right Triangles Investigation1: Isosceles Right Triangle Investigation2: 30°-60°-90° Triangles

Lesson 9.4: Story Problems

Lesson 9.5: Distance in Coordinate Geometry Investigation: The Distance Formula

Lesson 9.6: Circles and the Pythagorean Theorem

Using Your Algebra Skills Radical Expressions

Possible Extension Explorations: A Pythagorean Fractal Ladder Climb

Project: Creating A Geometry Flip Book (p. 483) Have students graph quadrilaterals on a coordinate grid and use algebraic properties to determine the specific name of the quadrilateral.

Quiz Chapter 9 Test: Pythagorean Theorem Chapter 9 More Projects and Explorations: Key Curriculum Resources



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Domain: Geometric Measurement and Dimension G-GMD Cluster: Explain volume formulas and use them to solve problems Standards: 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. Use dissection arguments, Cavalieri’s principle, and informal limit arguments.

2. (+) Give an informal argument, using Cavalieri’s principle for the formulas for the volume of a sphere and other solid figures.

3. Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.*

Domain: Modeling with Geometry G-MG Cluster: Apply geometric concepts in modeling situations Standards: 1. Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).*

2. Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot).*

Chapter 10: Volume Lesson 10.1: The Geometry of Solids

Lesson 10.2: Volume of Prisms and Cylinders Investigation: The Volume Formula for Prisms and Cylinders

Lesson 10.3: Volume of Pyramids and Cones Investigation: The Volume Formula for Pyramids and Cones

Lesson 10.4: Volume Problems

Lesson 10.5: Displacement and Density

Lesson 10.6: Volume of a Sphere Investigation: The Formula for the Volume of a Sphere

Lesson 10.7: Surface Area of a Sphere Investigation: The Formula for the Surface Area of a Sphere

Using Your Algebra Skills Solving for Any Variable

Possible Extension Explorations: Euler’s Formula for Polyhedrons The Five Platonic Solids Orthographic Drawing Sherlock Holmes and Forms of Valid Reasoning

CABS: Chubby’s Checkers Marzano’s Building Academic Vocabulary: Have students create a word wall including terms, descriptions, and visual representations to refer back to throughout the course. Use strategies such as: Talk-A-Mile-A-Minute Charades Pictionary Graphic Organizers I Have, Who Has

Quiz Chapter 10 Test: Volume Chapter 10 More Projects and Explorations: Key Curriculum Resources



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Domain: Congruence G-CO Cluster: Experiment with transformations in the plane Standards: 2. Represent transformations in the plane; 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. 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 another.

Domain: Similarity, Right Triangles and Trigonometry G-SRT Cluster: Understand similarity in terms of similarity transformations

Standards: 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 ratio given by the scale factor. 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 3. Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.

Cluster: Prove theorems involving similarity Standards: 4. Prove theorems about triangles. 5. Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

Domain: Circles G-C Cluster: Understand and apply theorems about circles Standard: 1.Prove that all circles are similar

Domain: Expressing Geometric Properties with Equations G-GPE Cluster: Use coordinates to prove simple geometric theorems algebraically Standards: 6. Find the point on a directed line segment between two given points that partitions the segment in a given ratio

Chapter 11: Similarity Lesson 11.1: Similar Polygons Investigation1: What Makes Polygons Similar? Investigation2: Dilations on the Coordinate Plane

Lesson 11.2: Similar Triangles Investigation1: Is AA a Similarity Shortcut? Investigation2: Is SSS a Similarity Shortcut? Investigation3: Is SAS a Similarity Shortcut?

Lesson 11.3: Indirect Measurement with Similar Triangles Investigation: Mirror, Mirror

Lesson 11.4: Corresponding Parts of Similar Triangles Investigation1: Corresponding Parts Investigation2: Opposite Side Ratio

Lesson 11.5: Proportions with Area Investigation1: Area Ratios Investigation2: Surface Area Ratios

Lesson 11.6: Proportions with Volume Investigation: Volume Ratios

Lesson 11.7: Proportional Segments Between Parallel Lines Investigation1: Parallel and Proportionality Investigation2: Extended Parallel/Proportionality

Using Your Algebra Skills Proportion and Reasoning

Project: Making a Mural (p. 588) *This project is needed to address the modeling standard Exploration: Constructing a Dilation Design (p. 595) *This exploration is needed to address multiple standards Exploration: Why Elephants Have Big Ears (p. 620)

Quiz Chapter 11 Test: Similarity Chapter 11 More Projects and Explorations: Key Curriculum Resources



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Domain: Similarity, Right Triangle and Trigonometry G-SRT Cluster: Define trigonometric ratios and solve problems involving right triangles Standards: 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

7. Explain and use the relationship between the sine and cosine of complementary angles.

8. Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.


Chapter 12: Trigonometry Lesson 12.1: Trigonometric Ratios Investigation1: Trigonometric Tables

Lesson 12.2: Problem Solving with Right Triangles

Using Your Algebra Skills Transforming Functions

Possible Extension Explorations and Lessons: Indirect Measurement Trigonometric Ratios and the Unit Circle Three Types of Proofs Lesson 12.3: The Law of Sines Investigation1: Area of a Triangle Investigation2: The Law of Sines

Lesson 12.4: The Law of Cosines Lesson 12.5: Problem Solving with Trigonometry

Project: Light for All Seasons (p. 651) *This project is needed to address the modeling standard.

Quiz Chapter 12 Test: Trigonometry Chapter 12 More Projects and Explorations: Key Curriculum Resources



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Domain: Congruence G-CO Cluster: Prove geometric theorems Standards: 9. Prove theorems about lines and angles 10. Prove theorems about triangles 11. Prove theorems about parallelograms

Cluster: Make geometric constructions Standards: 12. Make formal geometric constructions with a variety of tools and methods

Domain: Similarity, Right Triangles and Trigonometry G-SRT Cluster: Prove theorems involving similarity

Standards: 4. Prove theorems about triangles using similarity transformations 5. Use triangle congruence and similarity criteria to solve problems and to prove relationships in geometric figures

Domain: Circles G-C Cluster: Understand and apply theorems about circles Standard: 3. Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle

Domain: Expressing Geometric Properties with Equations G-GPE Cluster: Use coordinates to prove simple geometric theorems algebraically Standards: 4. Use coordinates to prove simple geometric theorems algebraically 5. Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems.

Chapter 13: Geometry as a Mathematical System Lesson 13.1: The Premises of Geometry

Lesson 13.2: Planning a Geometry Proof Lesson 13.3: Triangle Proofs Lesson 13.4: Quadrilateral Proofs Developing Proof: Proving Parallelogram Conjectures

Lesson 13.5: Indirect Proof Developing Proof: Proving the Tangent Conjecture

Lesson 13.6: Circle Proofs Lesson 13.7: Similarity Proofs Developing Proof: Proving the Tangent Conjecture

Possible Extension Explorations and Lessons: Non-Euclidean Geometries

Exploration: Proof as Challenge and Discovery (p. 720) Using Your Algebra Skills Coordinate Proof (p.736) *This assignment is needed to address multiple standards

Quiz Chapter 13 Test: Geometry as a Mathematical System Chapter 13 More Projects and Explorations: Key Curriculum Resources



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