Westbrook's Geometry

Teacher

Geometry

Last Updated 19 Mar 2009

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

**Geometry **
**Power Point Presentations**

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 |

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 2-4, Postulate 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 2-5, Theorem 2-6, Theorem 2-7, Theorem 2-8

Chapter 3, **
Using Perpendicular and Parallel Lines**,
Vocabulary

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 |

Chapter 4, **
Identifying Congruent Triangles**,
Vocabulary

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 |

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) |

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 7-9, Theorem 7-10, Theorem 7-11 (Angle Bisector Theorem) | Section 7-6,
Fractals and Self-Similarity,
Sample Problems |

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 (45^{o}-45^{o}-90^{o}),
Theorem 8-7 (30^{o}-60^{o}-90^{o}),
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 |

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 |

Chapter 10, **
Exploring Polygons and Area**,
Vocabulary

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 |

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 |

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) |

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 |