A unique and effective way to learn Geometry―updated with the latest instruction and review
Must Know High School Geometry provides a fresh approach to learning. As part of our Must Know series, this new edition makes sure what you really need to know is clear up-front. Rather than starting with goals to be met, chapters begin by telling you the most important concepts about the topic at hand―and then show you exactly how these concepts help you accomplish your goals.
Written by expert geometry educators, Must Know High School Geometry, Second Edition provides updated lesson content and useful examples to help clarify each topic. Every chapter closes with reinforcing exercises to get you the practice you need to gain confidence. New features to this edition focus on extra support and helping you avoid common mistakes. In the end, you get everything you need to build your geometry skills quickly and painlessly.
Features:
- More than 250 practice questions that parallel what you will find in your classwork and on exams
- Bonus app that includes 100+ flashcards to reinforce concepts
- “Extra Help” and “Easy Mistake” features put the emphasis on how to improve and what pitfalls to avoid
- Geometry topics aligned to national and state educational standards
- Practical examples throughout and an answer key with explanations make sure you understand the topics
- Conversational writing style and informative IRL (In Real Life) and BTW (By the Way) sidebars
- A special section for teachers with tips and strategies on teaching the material and content-specific links and resources
Author(s): Allen Ma, Amber Kuang
Edition: 2
Publisher: McGraw Hill
Year: 2022
Language: English
Pages: 496
Tags: Geometry; Triangle Proofs; Transformations; Triangles; Circle Theorems; Coordinate Geometry; Parallelograms;
Cover
Title Page
Copyright Page
Dedication
Contents
Introduction
The Flashcard App
1 Definitions
The Basics
Bisectors and Midpoints
Types of Angles
Reflexive, Substitution, and Transitive Properties
Addition and Subtraction Postulates
Exercises
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
Exercises
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
Exercises
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
Exercises
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
Exercises
6 Getting to Know Right Triangles
The Pythagorean Theorem
Pythagorean Triples
Special Right Triangles
Right Triangle Trigonometry
Word Problems
Exercises
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
Exercises
8 Parallelograms
Rectangles
Rhombuses
Squares
Trapezoids
Median of a Trapezoid
Exercises
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
Exercises
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
Exercises
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
Exercises
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
Exercises
13 Volume of Three-Dimensional Shapes
Cones
Cylinders
Prisms
Square Pyramids
Spheres
From 2D to 3D
Exercises
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
Exercises
Answer Key
Teacher’s Guide
