Must Know High School Geometry
Published on 4. July 2019
Book
Paperback/Softback
496 pages
978-1-260-45428-4 (ISBN)
Description
Publisher's Note: Products purchased from Third Party sellers are not guaranteed by the publisher for quality, authenticity, or access to any online entitlements included with the product.
A UNIQUE NEW APPROACH THAT'S LIKE A LIGHTNING BOLT TO THE BRAIN
You know that moment when you feel as though a lightning bolt has hit you because you finally get something? That's how this book will make you react. (We hope!) Each chapter makes sure that what you really need to know is clear right off the bat and sees to it that you build on this knowledge. Where other books ask you to memorize stuff, we're going to show you the must know ideas that will guide you toward success in geometry. You will start each chapter learning what the must know ideas behind a geometry subject are, and these concepts will help you solve the geometry problems that you find in your classwork and on exams.
Dive into this book and find:
* 250+ practice questions that mirror what you will find in your classwork and on exams* A bonus app with 100+ flashcards that will reinforce what you've learned* Extensive examples that drive home essential concepts* An easy-access setup that allows you to jump in and out of subjects* Geometry topics aligned to national and state education standards* Special help for more challenging geometry subjects, including proofs, transformations, and constructions
We're confident that the must know ideas in this book will have you up and solving geometry problems in no time-or at least in a reasonable amount of time!
The authors, between them, teach high school math courses including geometry, trigonometry, pre-calculus, calculus, and discrete math. Whew!
A UNIQUE NEW APPROACH THAT'S LIKE A LIGHTNING BOLT TO THE BRAIN
You know that moment when you feel as though a lightning bolt has hit you because you finally get something? That's how this book will make you react. (We hope!) Each chapter makes sure that what you really need to know is clear right off the bat and sees to it that you build on this knowledge. Where other books ask you to memorize stuff, we're going to show you the must know ideas that will guide you toward success in geometry. You will start each chapter learning what the must know ideas behind a geometry subject are, and these concepts will help you solve the geometry problems that you find in your classwork and on exams.
Dive into this book and find:
* 250+ practice questions that mirror what you will find in your classwork and on exams* A bonus app with 100+ flashcards that will reinforce what you've learned* Extensive examples that drive home essential concepts* An easy-access setup that allows you to jump in and out of subjects* Geometry topics aligned to national and state education standards* Special help for more challenging geometry subjects, including proofs, transformations, and constructions
We're confident that the must know ideas in this book will have you up and solving geometry problems in no time-or at least in a reasonable amount of time!
The authors, between them, teach high school math courses including geometry, trigonometry, pre-calculus, calculus, and discrete math. Whew!
More details
Language
English
Place of publication
OH
United States
Target group
College/higher education
Interest Age: From 13 to 17 years
Illustrations
200 Illustrations
Weight
674 gr
ISBN-13
978-1-260-45428-4 (9781260454284)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Persons
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.
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.
Content
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 degrees
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
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 degrees
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