CliffsNotes Geometry Common Core Quick Review

by M. Sunil R. Koswatta

Overview

A quick in, quick out review of Geometry Common Core math

Relevant to high school students enrolled in their Geometry class in those states adhering to the Common Core math standards, this quick review provides targeted chapter-level reviews of topics aligned to the Geometry Common Core math standards. The lessons are reinforced with practice problems throughout each chapter as well as chapter-end quizzes.

This quick review is supplemented with 300+ multiple-choice questions available on CliffsNotes.com.

Product Details

ISBN-13:	9780544883741
Publisher:	Houghton Mifflin Harcourt
Publication date:	06/13/2017
Sold by:	Houghton Mifflin Harcourt
Format:	eBook
Pages:	224
File size:	7 MB

About the Author

M. SUNIL R. KOSWATTA, Ph.D. Mathematics, has been an educator and mathematics curriculum writer for 25 years. Dr. Koswatta has mentored K–12 teachers on the Common Core Standards and was a member of the EngageNY Common Core curriculum writing team. He has conducted Teacher Training Institutes at the University of California at Berkeley for over 12 years, and has coordinated presentations on the Common Core Standards for the Illinois Mathematics Association of Community Colleges. He is currently a mathematics professor at Harper College in Illinois.

Table of Contents

Introduction 1

Common Core State Standards for Mathematics (CCSSM) 1

Connecting to Common Core Mathematics 2

Why You Need This Book 3

How to Use This Book 3

Hundreds of Practice Questions Online! 4

Chapter 1 Fundamental Ideas 5

Points, Lines, and Planes 6

Point 6

Line 6

Plane 7

Set 7

Postulates and Theorems 7

Segments, Midpoints, and Rays 9

Line segment 9

Midpoint 10

Ray 11

Angles 11

Adjacent angles 13

Circles 13

Central angles, sectors, and arcs 13

Special Angles 15

Right angle 15

Acute angle 15

Obtuse angle, 16

Complementary angles 17

Supplementary angles 18

Parallel, Intersecting, and Perpendicular Lines 19

Parallel lines in a plane 19

Intersecting lines 19

Perpendicular lines 20

Angle bisector and perpendicular bisector 21

Triangles, Quadrilaterals, and Polygons 21

Special triangles and quadrilaterals 23

Chapter 2 Basic Rigid Motions 25

Rotations 26

Counterclockwise rotation p of θ degrees around O 26

Clockwise rotation p of θ degrees around O 26

Transversals 30

Reflections 36

Translations 37

Chapter 3 Triangles and Congruence 41

Exterior Angle of a Triangle 42

Angle Sum of a Triangle 44

Classifying Triangles by Sides or Angles 44

Special names for sides and angles 45

Altitudes, Medians, and Angle Bisectors 46

Base and altitude 46

Median 47

Angle bisector 48

Special Features of Isosceles Triangles 48

Triangle Inequalities Regarding Sides and Angles 51

The Triangle Inequality Theorem 52

The Concept of Congruence 53

Corresponding Parts of Triangles 55

Congruence theorems of triangles 55

Chapter 4 Polygons 65

Triangulation of a Polygon and the Sum of the Interior Angles 65

Exterior Angles of a Convex Polygon 67

Regular Polygons 69

Parallelograms 70

Rectangles 72

Rhombus 72

Trapezoids 74

The Midpoint Theorem 77

Concurrence Theorems 78

Chapter 5 Similarity 83

Dilation 84

The Fundamental Theorem of Similarity 85

The Definition of Similarity 88

Similar Triangles 89

Applications of Similarity 92

Proportional Parts of Similar Triangles 97

Pythagorean Theorem 98

Chapter 6 Circles 103

Parts of Circles 103

Arcs 104

Arcs and Inscribed Angles 110

Concyclic Points 117

Segments of Intersecting Chords and Tangenrs 121

Chapter 7 Length and Area 127

Length of a Line Segment 128

Length of a Polygonal Curve 129

Squares and Rectangles 130

Triangles 134

Right triangles 134

Arbitrary triangles 135

Parallelograms 137

Trapezoids 138

Regular Polygons 140

Parts of a regular polygon 140

Finding the perimeter 141

Finding the area 141

Effect of a dilation of scale factor r on the area of a polygon 142

Area and Circumference of a Circle 143

Summary of Perimeter, Circumference, and Area Formulas 148

Chapter 8 Geometric Solids 151

Prisms 151

Right Prisms 152

Lateral area of a right prism 152

Total surface area of a right prism 153

Interior space of a solid 154

Right Circular Cylinders 156

Pyramids 158

Regular pyramids 158

Right Circular Cones 161

Spheres 164

Summary of Lateral Area, Total Area, and Volume Formulas 165

Chapter 9 Coordinate Geometry 167

One-Dimensional Distance Formula 171

Two-Dimensional Distance Formula 171

Midpoint Formula for One-Dimensional Space 174

Midpoint Formula for Two-Dimensional Space 174

Equation of a Circle 176

Lines on a Coordinate Plane 178

The Slope Theorem 180

Slopes of parallel lines 184

Slopes of perpendicular lines 187

Linear Equations in x and y 190

Summary of Coordinate Geometry Formulas 199

Review Questions 201

Glossary 213

Appendix: Postulates and Theorems 221

Postulates 221

Theorems 222

Chapter 1 Fundamental Ideas 222

Chapter 2 Basic Rigid Motions 223

Chapter 3 Triangles and Congruence 224

Chapter 4 Polygons 226

Chapter 5 Similarity 227

Chapter 6 Circles 229

Chapter 7 Length and Area 231

Chapter 8 Geometric Solids 232

Chapter 9 Coordinate Geometry 234

Index 237