Geometry, Grades 9-11: Mcdougal Littell Geometry

, by Holt Mcdougal

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ISBN: 9780395977279 | 0395977274
Cover: Hardcover
Copyright: 1/26/1999

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Points, Lines, Planes, and Angles

Some Basic Figures

A Game and Some Geometry

(4)

Points, Lines, and Planes

(6)

Definitions and Postulates

Segments, Rays, and Distance

(6)

Angles

(5)

Postulates and Theorems Relating Points, Lines, and Planes

(11)

Deductive Reasoning

Using Deductive Reasoning

If-Then Statements; Converses

(4)

Properties from Algebra

(6)

Proving Theorems

(7)

Theorems about Angles and Perpendicular Lines

Special Pairs of Angles

(6)

Perpendicular Lines

(4)

Planning a Proof

(13)

Parallel Lines and Planes

When Lines and Planes Are Parallel

Definitions

(5)

Properties of Parallel Lines

(5)

Proving Lines Parallel

(10)

Applying Parallel Lines to Polygons

Angles of a Triangle

(8)

Angles of a Polygon

101

(5)

Inductive Reasoning

106

(11)

Congruent Triangles

Corresponding Parts in a Congruence

Congruent Figures

117

(5)

Some Ways to Prove Triangles Congruent

122

(5)

Using Congruent Triangles

127

(7)

Some Theorems Based on Congruent Triangles

The Isosceles Triangle Theorems

134

(6)

Other Methods of Proving Triangles Congruent

140

(6)

More about Proof in Geometry

Using More than One Pair of Congruent Triangles

146

(6)

Medians, Altitudes, and Perpendicular Bisectors

152

(15)

Quadrilaterals

Parallelograms

Properties of Parallelograms

167

(5)

Ways to Prove that Quadrilaterals Are Parallelograms

172

(5)

Theorems Involving Parallel Lines

177

(7)

Special Quadrilaterals

Special Parallelograms

184

(6)

Trapezoids

190

(13)

Inequalities In Geometry

Inequalities and Indirect Proof

Inequalities

203

(5)

Inverses and Contrapositives

208

(6)

Indirect Proof

214

(5)

Inequalities in Triangles

Inequalities for One Triangle

219

(9)

Inequalities for Two Triangles

228

(13)

Similar Polygons

Ratio, Proportion, and Similarity

Ratio and Proportion

241

(4)

Properties of Proportions

245

(3)

Similar Polygons

248

(6)

Working with Similar Triangles

A Postulate for Similar Triangles

254

(9)

Theorems for Similar Triangles

263

(6)

Proportional Lengths

269

(16)

Right Triangles

Similarity in Right Triangles

285

(5)

The Pythagorean Theorem

290

(5)

The Converse of the Pythagorean Theorem

295

(5)

Special Right Triangles

300

(5)

Trigonometry

The Tangent Ratio

305

(7)

The Sine and Cosine Ratios

312

(5)

Applications of Right Triangle Trigonometry

317

(12)

Circles

Tangents, Arcs, and Chords

Basic Terms

329

(4)

Tangents

333

(6)

Arcs and Central Angles

339

(5)

Arcs and Chords

344

(5)

Angles and Segments

Inscribed Angles

349

(8)

Other Angles

357

(4)

Circles and Lengths of Segments

361

(14)

Constructions and Loci

Basic Constructions

What Construction Means

375

(5)

Perpendiculars and Parallels

380

(6)

Concurrent Lines

386

(6)

More Constructions

Circles

392

(4)

Special Segments

396

(5)

Locus

The Meaning of Locus

401

(4)

Locus Problems

405

(5)

Locus and Construction

410

(13)

Areas of Plane Figures

Areas of Polygons

Areas of Rectangles

423

(6)

Areas of Parallelograms, Triangles, and Rhombuses

429

(6)

Areas of Trapezoids

435

(5)

Areas of Regular Polygons

440

(5)

Circles, Similar Figures, and Geometric Probability

Circumferences and Areas of Circles

445

(7)

Arc Lengths and Areas of Sectors

452

(4)

Ratios of Areas

456

(5)

Geometric Probability

461

(14)

Areas and Volumes of Solids

Important Solids

Prisms

475

(7)

Pyramids

482

(8)

Cylinders and Cones

490

(7)

Similar Solids

Spheres

497

(11)

Areas and Volumes of Similar Solids

508

(15)

Coordinate Geometry

Geometry and Algebra

The Distance Formula

523

(6)

Slope of a Line

529

(6)

Parallel and Perpendicular Lines

535

(4)

Vectors

539

(5)

The Midpoint Formula

544

(4)

Lines and Coordinate Geometry Proofs

Graphing Linear Equations

548

(5)

Writing Linear Equations

553

(3)

Organizing Coordinate Proofs

556

(4)

Coordinate Geometry Proofs

560

(11)

Transformations

Some Basic Mappings

Mappings and Functions

571

(6)

Reflections

577

(6)

Translations and Glide Reflections

583

(5)

Rotations

588

(4)

Dilations

592

(7)

Composition and Symmetry

Composites of Mappings

599

(6)

Inverses and the Identity

605

(4)

Symmetry in the Plane and in Space

609

(17)

Examinations

626

(14)

College Entrance Exams

640

(4)

Logic

644

(11)

Flow Proofs

655

(2)

Handbook for Integrating Coordinate and Transformational Geometry

657

(19)

Discrete Mathematics

676

(8)

Fractal Geometry

684

(8)

Postulates

692

(1)

Theorems

693

(8)

Constructions

701

(1)

Portfolio Projects

702

(8)

Constructions Using Paper Folding

710

(6)

Coordinates in Three Dimensions

716

(3)

Changing the Dimensions of Geometric Figures

719

(3)

Relationships Among Sine, Cosine, and Tangent

722

(4)

Glossary

726

(7)

Index

733

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Geometry, Grades 9-11: Mcdougal Littell Geometry

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