Must Know High School Geometry

Amber Kuang teaches high school honors pre-calculus, honors calculus, geometry 2/trigonometry, geometry, and discrete math. She is a New York State Regent Exams review instructor. Allen Ma teaches high school geometry, geometry, pre-calculus, and trigonometry. He is a recipient of the Nassau County Long Island Math Teacher of the Year award.

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