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Geometry Essentials For Dummies [Minkštas viršelis]

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  • Formatas: Paperback / softback, 196 pages, aukštis x plotis x storis: 211x135x15 mm, weight: 249 g
  • Išleidimo metai: 07-Jun-2011
  • Leidėjas: For Dummies
  • ISBN-10: 1118068750
  • ISBN-13: 9781118068755
Kitos knygos pagal šią temą:
Geometry Essentials For DummiesDidesnis paveikslėlis
  • Formatas: Paperback / softback, 196 pages, aukštis x plotis x storis: 211x135x15 mm, weight: 249 g
  • Išleidimo metai: 07-Jun-2011
  • Leidėjas: For Dummies
  • ISBN-10: 1118068750
  • ISBN-13: 9781118068755
Kitos knygos pagal šią temą:
Pastovi nuoroda: https://www.kriso.lt/db/9781118068755.html
Raktažodžiai:
Each book covers all the necessary information a beginner needs to know about a particular topic, providing an index for easy reference and using the series' signature set of symbols to clue the reader in to key topics, categorized under such titles as Tip, Remember, Warning!, Technical Stuff and True Story. Original.

Just the critical concepts you need to score high in geometry

This practical, friendly guide focuses on critical concepts taught in a typical geometry course, from the properties of triangles, parallelograms, circles, and cylinders, to the skills and strategies you need to write geometry proofs. Geometry Essentials For Dummies is perfect for cramming or doing homework, or as a reference for parents helping kids study for exams.

  • Get down to the basics — get a handle on the basics of geometry, from lines, segments, and angles, to vertices, altitudes, and diagonals

  • Conquer proofs with confidence — follow easy-to-grasp instructions for understanding the components of a formal geometry proof

  • Take triangles in strides — learn how to take in a triangle's sides, analyze its angles, work through an SAS proof, and apply the Pythagorean Theorem

  • Polish up on polygons — get the lowdown on quadrilaterals and other polygons: their angles, areas, properties, perimeters, and much more

Open the book and find:

  • Plain-English explanations of geometry terms

  • Tips for tackling geometry proofs

  • The seven members of the quadrilateral family

  • Straight talk on circles

  • Essential triangle formulas

  • The lowdown on 3-D: spheres, cylinders, prisms, and pyramids

  • Ten things to use as reasons in geometry proofs

Learn to:

  • Core concepts about the geometry of shapes and geometry proofs

  • Critical theorems, postulates, and definitions

  • The principles and formulas you need to know

Introduction 1(4)
About This Book
1(1)
Conventions Used in This Book
2(1)
Foolish Assumptions
2(1)
Icons Used in This Book
3(1)
Where to Go from Here
3(2)
Chapter 1 An Overview of Geometry
5(16)
The Geometry of Shapes
6(1)
One Dimensional shapes
6(1)
Two Dimensional shapes
6(1)
Three Dimensional shapes
6(1)
Geometry Proofs
6(1)
Am I Ever Going to Use This?
7(2)
When you'll use your knowledge of shapes
8(1)
When you'll use your knowledge of proofs
8(1)
Getting Down with Definitions
9(2)
A Few Points on Points
11(1)
Lines, Segments, and Rays
12(2)
Horizontal and vertical lines
13(1)
Doubling up with pairs of lines
13(1)
Coplanar lines
13(1)
Non-coplanar lines
14(1)
Investigating the Plane Facts
14(1)
Everybody's Got an Angle
15(3)
Five types of angles
15(1)
Angle pairs
16(2)
Bisection and Trisection
18(3)
Segments
18(1)
Angles
19(2)
Chapter 2 Geometry Proof Starter Kit
21(20)
The Lay of the (Proof) Land
21(1)
Reasoning with If-Then Logic
22(5)
If-then chains of logic
23(2)
Definitions, theorems, and postulates
25(1)
Using definitions in the reason column
25(1)
Using theorems and postulates as reasons
25(2)
Bubble logic
27(1)
Complementary and Supplementary Angles
27(3)
Addition and Subtraction
30(5)
Addition theorems
30(4)
Subtraction theorems
34(1)
Like Multiples and Like Divisions
35(2)
Congruent Vertical Angles
37(1)
Transitivity and Substitution
38(3)
Chapter 3 Tackling a Longer Proof
41(10)
Making a Game Plan
42(1)
Using All the Givens
42(1)
Using If-Then Logic
43(2)
Chipping Away at the Problem
45(2)
Working Backward
47(2)
Filling In the Gaps
49(1)
Writing Out the Finished Proof
49(2)
Chapter 4 Triangle Fundamentals
51(18)
Taking In a Triangle's Sides
51(1)
Scalene triangles
52(1)
Isosceles triangles
52(1)
Equilateral triangles
52(1)
Triangle Classification by Angles
52(1)
The Triangle Inequality Principle
53(1)
Sizing Up Triangle Area
54(3)
A triangle's altitude or height
54(2)
Determining a triangle's area
56(1)
Regarding Right Triangles
57(1)
The Pythagorean Theorem
58(2)
Pythagorean Triple Triangles
60(4)
The Fab Four triangles
61(1)
Families of Pythagorean triple triangles
61(1)
No-brainer cases
61(1)
The step-by-step triple triangle method
62(2)
Two Special Right Triangles
64(5)
The 45°- 45°- 90° triangle
64(2)
The 30°- 60°- 90° triangle
66(3)
Chapter 5 Congruent Triangle Proofs
69(16)
Proving Triangles Congruent
69(6)
SSS: The side-side-side method
70(2)
SAS: side-angle-side
72(2)
ASA: The angle-side-angle tack
74(1)
AAS: angle-angle-side
74(1)
Last but not least: HLR
75(1)
Taking the Next Step with CPCTC
75(4)
Defining CPCTC
76(1)
Tackling a CPCTC proof
76(3)
The Isosceles Triangle Theorems
79(2)
The Two Equidistance Theorems
81(4)
Determining a perpendicular bisector
81(2)
Using a perpendicular bisector
83(2)
Chapter 6 Quadrilaterals
85(22)
Parallel Line Properties
85(4)
Parallel lines with a transversal
85(2)
The transversal theorems
87(2)
The Seven Special Quadrilaterals
89(1)
Working with Auxiliary Lines
90(3)
The Properties of Quadrilaterals
93(7)
Properties of the parallelogram
93(2)
Properties of the three special parallelograms
95(3)
Properties of the kite
98(1)
Properties of the trapezoid and the isosceles trapezoid
99(1)
Proving That You've Got a Particular Quadrilateral
100(7)
Proving you've got a parallelogram
100(3)
Proving that you've got a rectangle, rhombus, or square
103(1)
Proving that you've got a kite
104(3)
Chapter 7 Polygon Formulas
107(12)
The Area of Quadrilaterals
107(6)
Quadrilateral area formulas
107(1)
Why the formulas work
108(2)
Trying a few area problems
110(1)
Locating special right triangles in parallelograms
110(1)
Using triangles and ratios in a rhombus problem
111(1)
Drawing in diagonals to find a kite's area
112(1)
The Area of Regular Polygons
113(3)
The polygon area formulas
114(1)
Tackling an area problem
114(2)
Angle and Diagonal Formulas
116(3)
Interior and exterior angles
116(1)
A polygon angle problem
117(1)
Criss-crossing with diagonals
118(1)
Chapter 8 Similarity
119(16)
Similar Figures
119(6)
Defining similar polygons
119(2)
How similar figures line up
121(2)
Solving a similarity problem
123(2)
Proving Triangles Similar
125(4)
Tackling an AA proof
125(1)
Using SSS
126(2)
An SAS- proof
128(1)
Splitting Right Triangles with the Altitude-on-Hypotenuse Theorem
129(2)
More Proportionality Theorems
131(4)
The Side-Splitter Theorem
131(2)
The Angle-Bisector Theorem
133(2)
Chapter 9 Circle Basics
135(16)
Radii, Chords, and Diameters
135(3)
Five circle theorems
136(1)
Using extra radii
136(2)
Arcs and Central Angles
138(1)
Tangents
138(2)
The Pizza Slice Formulas
140(4)
Determining arc length
140(1)
Sector and segment area
141(3)
The Angle-Arc Formulas
144(4)
Angles on a circle
144(1)
Angles inside a circle
145(1)
Angles outside a circle
145(1)
Keeping the formulas straight
146(2)
The Power Theorems
148(3)
The Chord-Chord Theorem
148(1)
The Tangent-Secant Theorem
149(1)
The Secant-Secant Theorem
149(1)
Condensing the power theorems into a single idea
150(1)
Chapter 10 3-D Geometry
151(10)
Flat-Top Figures
151(3)
Pointy-Top Figures
154(5)
Spheres
159(2)
Chapter 11 Coordinate Geometry
161(10)
The Coordinate Plane
161(1)
Slope, Distance, and Midpoint
162(5)
The slope dope
162(2)
The distance formula
164(1)
The midpoint formula
165(1)
Trying out the formulas
165(2)
Equations for Lines and Circles
167(4)
Line equations
167(1)
The circle equation
168(3)
Chapter 12 Ten Big Reasons to Use in Proofs
171(4)
The Reflexive Property
171(1)
Vertical Angles Are Congruent
171(1)
The Parallel-Line Theorems
172(1)
Two Points Determine a Line
172(1)
All Radii Are Congruent
173(1)
If Sides, Then Angles
173(1)
If Angles, Then Sides
173(1)
Triangle Congruence
173(1)
CPCTC
174(1)
Triangle Similarity
174(1)
Index 175
Mark Ryan owns and operates The Math Center in Chicago and is the author of Calculus For Dummies and several other math books.