Cover

Title Page

Copyright Page

Dedication

Authors’ Acknowledgments

Contents

Introduction

The Flashcard App

1 Definitions

The Basics

Bisectors and Midpoints

Types of Angles

Reflexive, Substitution, and Transitive Property

Addition and Subtraction Postulate

2 Triangle Proofs

Side-Side-Side Postulate for Proving Triangles Congruent

Side-Angle-Side Postulate for Proving Triangles Congruent

Angle-Side-Angle Postulate for Proving Triangles Congruent

Angle-Angle-Side Postulate for Proving Triangles Congruent

Why Is Side-Side-Angle Not a Postulate for Proving Triangles Congruent?

Why Is Angle-Angle-Angle Not a Postulate for Proving Triangles Congruent?

Hypotenuse-Leg Postulate for Proving Triangles Congruent

Corresponding Parts of Congruent Triangles Are Congruent

3 Classifying Triangles

Solving for the Angles in a Triangle

Exterior Angle Theorem

Classifying Triangles by Angle Measurements

Isosceles, Equilateral, and Scalene Triangles

Relationships of the Sides and Angles of Triangles

Median, Altitude, and Angle Bisector

4 Centers of a Triangle

Centroid of a Triangle

The Incenter of a Triangle

The Orthocenter of a Triangle

The Circumcenter of a Triangle

The Euler Line

5 Similarity

Proportions in Similar Triangles

Determining Whether Triangles Are Similar

Perimeter and Area of Similar Triangles

Parallel Lines Inside a Triangle

Proportions of Similar Right Triangles

Similar Triangle Proofs

6 Getting to Know Right Triangles

The Pythagorean Theorem

Pythagorean Triples

Special Right Triangles

Right Triangle Trigonometry

Word Problems

7 Parallel Lines

Alternate Interior Angles

Corresponding Angles

Alternate Exterior, Same-Side Interior, and Same-Side Exterior Angles

Auxiliary Lines

Proving That the Sum of the Angles of a Triangle Is 180°

Determining If Lines Are Parallel

8 Parallelograms

Rectangles

Rhombuses

Squares

Trapezoids

Median of a Trapezoid

9 Coordinate Geometry

Distance Formula

Using the Distance Formula to Classify Shapes

Midpoint Formula

Slope Formula

Writing the Equations of Parallel and Perpendicular Lines

Partitioning a Line Segment

10 Transformations

Reflections

Reflection Over the Y-Axis

Reflection Over the X-Axis

Reflection Over the Line y = x

Reflecting a Point Over Horizontal and Vertical Lines

Reflecting a Point Over an Oblique Line

Finding the Equation for the Line of Reflection

Point Reflections

Rotations

Summary of Rules for Rotations with the Center of Rotation at the Origin

Rotation with Center of Rotation Not at the Origin

Translations

Dilation

Dilations Not Centered at the Origin

Composition of Transformations

11 Circle Theorems Involving Angles and Segments

Definition of Terms Related to a Circle

Lengths of Intersecting Chords

Finding the Length of Secant Segments

Length of Tangent–Secant Segments from an External Point

Angles Associated with the Circle

Central Angle

Inscribed Angle

Angle Formed by Two Intersecting Chords

Exterior Angles of a Circle

12 Circumference and the Area of Circles

Finding the Area of a Sector

Finding the Length of the Arc of a Sector

Standard Form of a Circle

General Form of a Circle

Graphing a Circle on the Coordinate Plane

13 Volume of Three-Dimensional Shapes

Cones

Cylinders

Prisms

Square Pyramids

Spheres

From 2D to 3D

14 Constructions

Copying Segments and Angles

Bisectors and Perpendicular and Parallel Lines

Constructions Involving Perpendicular Lines

Constructing Parallel Lines

Construction Applications

Constructing an Altitude and a Median

Constructing a Square and Hexagon Inscribed in a Circle

Constructing Transformations

Answer Key