Westbrook's Geometry



Last Updated 19 Mar 2009

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  The Chapter links are access to vocabulary, postulates, theorems, and corollaries.

Perspective Drawing Paper  Theorem Flash Cards

Geometry Power Point Presentations

Discovering Points, Lines, Planes, and Angles Connecting Reasoning and Proof
Using Perpendicular and Parallel Lines Identifying Congruent Triangles
Applying Congruent Triangles Exploring Quadrilaterals
Connecting Proportion and Similarity Applying Right Triangles and Trigonometry
Analyzing Circles Exploring Polygons and Area
Investigating Surface Area and Volume Continuing Coordinate Geometry
Investigating Loci and Coordinate Transformations  


Chapter 1, Discovering Points, Lines, Planes, and Angles, Vocabulary

Section 1-1, The Coordinate Plane

Section 1-2, Points, Lines, and Planes

Section 1-3, Using Formulas

Section 1-4, Measuring Segments, Postulate 1-1, Postulate 1-2, Pythagorean Theorem, Distance Formula

Section 1-5, Midpoint and Segment Congruence, Midpoint Formula, Theorem 1-1 (The Midpoint Theorem)

Section 1-6, Exploring Angles, Postulate 1-3 (Protractor Postulate), Postulate 1-4 (Angle Addition Postulate)

Section 1-7, Angle Relationships

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Chapter 2, Connecting Reasoning and Proof, Vocabulary

Section 2-1, Inductive Reasoning and Conjecturing, Inductive Reasoning Section 2-2, If-Then Statements and Postulates, Postulate 2-1, Postulate 2-2,  Postulate 2-3, Postulate 2-4Postulate 2-5, Postulate 2-6
Section 2-3, Deductive Reasoning, Law of Detachment, Law of Syllogism Section 2-4, Using Proofs in Algebra, Properties of Equality for Real Numbers
Section 2-5, Verifying Segment Relationships, Theorem 2-1 Section 2-6, Verifying Angle Relationships, Theorem 2-2 (Supplement Theorem), Theorem 2-3, Theorem 2-4,  Theorem 2-5Theorem 2-6,  Theorem 2-7,  Theorem 2-8

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Chapter 3, Using Perpendicular and Parallel LinesVocabulary

Section 3-1, Parallel Lines and Transversals, Skew lines, Two lines cut by a transversal Section 3-2, Angles and Parallel Lines, Postulate 3-1(Corresponding Angles Postulate), Theorem 3-1 (Alternate Interior Angles Theorem), Theorem 3-2 (Consecutive Interior Angles Theorem), Theorem 3-3 (Alternate Interior Angles Theorem), Theorem 3-4 (Perpendicular Transversal Theorem)
Section 3-3, Slopes of Lines, Definition of Slope, Postulate 3-2, Postulate 3-3 Section 3-4, Proving Lines are Parallel, Postulate 3-4, Postulate 3-5 (Parallel Postulate), Theorem 3-5, Theorem 3-6, Theorem 3-7, Theorem 3-8
Section 3-5, Parallels and Distance,  Definition of Distance Between A point and a Line, Definition of Distance Between Parallel Lines Section 3-6, Spherical Geometry

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Chapter 4, Identifying Congruent TrianglesVocabulary

Section 4-1, Classifying Triangles, Definition of Isosceles Triangle Section 4-2, Measuring Angles in Triangles, Theorem 4-1 (Angle Sum theorem), Theorem 4-2 (Third Angle Theorem),  Theorem 4-3 (Exterior Angle theorem), Corollary 4-1, Corollary 4-2
Section 4-3,  Exploring Congruent Triangles, Theorem 4-4 Section 4-4,  Proving Triangles Congruent, Postulate 4-1 (SSS Postulate), Postulate 4-2 (SAS Postulate), Postulate 4-3 (ASA Postulate)
Section 4-5, More Congruent Triangles, Theorem 4-5 (AAS Theorem) Section 4-6,  Analyzing Isosceles Triangles, Theorem 4-6 (Isosceles Triangle Theorem), Theorem 4-7, Corollary 4-3, Corollary 4-4

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Chapter 5, Applying Congruent Triangles, Vocabulary

Section 5-1, Special Segments in Triangles, Theorem 5-1, Theorem 5-2,  Theorem 5-3, Theorem 5-4 Section 5-2, Right Triangles, Theorem 5-5 (LL), Theorem 5-6 (HA), Theorem 5-5 (LA), Postulate 5-1 (HL),
Section 5-3, Indirect Proof and Inequalities, Steps For a Writing an Indirect Proof, Theorem 5-8 (Exterior Angle Inequality Theorem), Definition of Inequality Section 5-4, Inequalities for Sides and Angles of a Triangle,Theorem 5-9, Theorem 5-10, Theorem 5-11, Corollary 5-1
Section 5-5, The Triangle Inequality, Theorem 5-12 (Triangle Inequality Theorem) Section 5-6, Inequalities Involving Two Triangles, Theorem 5-13 (SAS Inequality, Hinge Theorem), Theorem 5-14 (SSS Inequality)

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Chapter 6, Exploring Quadrilaterals, Vocabulary

Section 6-1, Parallelograms, Theorem 6-1, Theorem 6-2, Theorem 6-3, Theorem 6-4 Section 6-2, Tests fro Parallelograms, Theorem 6-5, Theorem 6-6, Theorem 6-7, Theorem 6-8
Section 6-3, Rectangles, Theorem 6-9, Theorem 6-10 Section 6-4, Squares and Rhombi, Theorem 6-11, Theorem 6-12, Theorem 6-13
Section 6-5, Trapezoids, Theorem 6-14, Theorem 6-15, Theorem 6-16  


Chapter 7, Connecting Proportion and Similarity, Vocabulary

Section 7-1, Using Proportions, Equality of Cross Product Section 7-2, Exploring Similar Polygons, Definition of Similar Polygon
Section 7-3, Identifying Similar Triangles, Postulate 7-1 (AA Similarity), Theorem 7-1 (SSS Similarity), Theorem 7-2 (SAS Similarity), Theorem 7-3 Section 7-4, Parallel Lines and Proportional Parts, Theorem 7-4 (Triangle Proportionality), Theorem 7-5, Theorem 7-6, Corollary 7-1,                Corollary 7-2
Section 7-5, Parts of Similar Triangles, Theorem 7-4 (Proportional Perimeters),  Theorem 7-8, Theorem 7-9Theorem 7-10, Theorem 7-11 (Angle Bisector Theorem) Section 7-6, Fractals and Self-Similarity, Sample Problems

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Chapter 8, Applying Right Triangles and Trigonometry, Vocabulary

Section 8-1, Geometric Mean and the Pythagorean Theorem, Theorem 8-1, Theorem 8-2, Theorem 8-3, Theorem 8-4 (Pythagorean Theorem), Theorem 8-5 (Converse of Pythagorean Theorem), Pythagorean Triplet, Sample Problems Section 8-2, Special Right Triangles, Theorem 8-6 (45o-45o-90o), Theorem 8-7 (30o-60o-90o), Sample Problems
Section 8-3, Ratios in Right Triangles, (Trig Ratios), Sample Problems Section 8-4, Angles of Elevation and Depression, (Angle of Elevation/Depression), Sample Problems
Section 8-5, Using the Law of Sines, Definition of Law of Sines, Sample Problems Section 8-6, Using the Law of Cosines, Definition of Law of Cosines, Sample Problems

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Chapter 9, Analyzing Circles, Vocabulary

Section 9-1, Exploring Circles, Circumference of Circle, Sample Problems Section 9-2, Angles and Arcs, Sum of Central Angles, Definition of Arc Measure, Postulate 9-1(Arc Addition Postulate), Sample Problems
Section 9-3, Arcs and Chords, Theorem 9-1, Theorem 9-2, Theorem 9-3, Sample Problems Section 9-4,  Inscribed Angles, Theorem 9-4, Theorem 9-5, Theorem 9-6,  Theorem 9-7, Sample Problems
Section 9-5, Exploring Tangents, Theorem 9-8, Theorem 9-9 (Converse of Theorem 9-8), Theorem 9-10, Sample Problems Section 9-6, Secants, Tangents, and Angle Measure, Theorem 9-11, Theorem 9-12, Theorem 9-13, Sample Problems
Section 9-7, Special Segments in a Circle, Theorem 9-14, Theorem 9-15, Theorem 9-16, Sample Problems Section 9-8, Equations of Circles, Standard Equation of a Circle, Sample Problems

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Chapter 10, Exploring Polygons and AreaVocabulary

Section 10-1, Polygons, Definition of Polygons, Definition of Regular Polygons, Theorem 10-1 (Interior Angle Sum Theorem), Theorem 10-2 (Exterior Angle Sum Theorem), Sample Problems Section 10-2, Tessellations, Sample Problems
Section 10-3, Area of Parallelograms, Postulate 10-1, Sample Problems Section 10-4, Area of Triangle, Rhombi, and Trapezoids, Postulate 10-2, Sample Problems
Section 10-5, Area of a Regular Polygon and Circles, Sample Problems Section 10-6, Geometric Probability, Postulate 10-3 (Length Probability Postulate), Postulate 10-4 (Area Probability Postulate), Area of a Sector of a Circle, Sample Problems
Section 10-7, Polygons as Networks, Network Traceability Tests, Starting Points for Network Traceability, Sample Problems  

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Chapter 11, Investigating Surface Area and Volume, Vocabulary

Section 11-1, Exploring Three-Dimensional Figures, (Definitions), Sample Problems Section 11-2, Nets and Surface Areas, Sample Problems
Section 11-3, Surface Area of Prisms and Cylinders, Lateral Area of a Right Prism, Surface Area of a Right Prism, Lateral Area of a Right Cylinder,  Surface Area of a Right Cylinder, Sample Problems Section 11-4,  Surface Area of Pyramids and Cones, Lateral Area of a Regular Pyramid, Surface Area of a Regular Pyramid, Lateral and Surface Area of a Right Circular Cone, Sample Problems
Section 11-5, Volume of Prisms and Cylinders, Volume of a Right Prism, Volume of a Right Cylinder Section 11-6, Volumes of Pyramids and Cones, Volume of a Right Circular Cone, Volume of a Right Pyramid, Cavalieri's Principle
Section 11-7, Surface Area of a Sphere, Volume of a Sphere Section 11-8, Congruent and Similar Solids

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Chapter 12, Continuing Coordinate Geometry, Vocabulary

Section 12-1, Graphing Linear Equations, Theorem 12-1 (Slope-Intercept form) Section 12-2, Writing Equations of Lines
Section 12-3, Scatter Plots and Slopes Section 12-4, Coordinate Proof, Guidelines for Placing Figures on a Coordinate Plane
Section 12-5, Vectors Section 12-6, Coordinates in Space, Theorem 12-2 (Three Dimensional Distance Formula)

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Chapter 13, Investigating Loci and Coordinate Transformations, Vocabulary

Section 13-1, What is a Locus?, Procedures for Determining Locus Section 13-2, Locus and System of Linear Equations
Section 13-3, Intersection of Loci Section 13-4, Mappings, Definition of Transformation, Definition of Isometry (Congruence Transformation)
Section 13-5, Reflections Section 13-6, Translations
Section 13-7, Rotations, Postulate 13-1 Section 13-8, Dilations, Theorem 13-1

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