Heath Geometry : An Integrated Approach

by Larson; Boswell; Stiff

• ISBN13: 9780669455304
• ISBN10: 066945530X
• Format: Hardcover
• Copyright: 1998-01-01
• Publisher: MCDOUG-LITTELL

Table of Contents

An Overview of Geometry
Chapter Overview	1	(1)
What is Geometry?	2	(1)
Exploring Optical Illusions	3	(6)
Exploring Shapes	9	(13)
Mixed Review: Algebra and Geometry	15	(1)
Career Interview: Commercial Pilot	15	(7)
Exploring Congruence and Similarity
Exploring Symmetry	22	(8)
Using a Computer Drawing Program: Exploring Congruence and Similarity	28	(1)
Mid-Chapter Partner Quiz	29	(1)
Coordinate Geometry and Noncoordinate Geometry	30	(6)
Exploring Measure	36	(8)
Mixed Review: Algebra and Geometry	41	(1)
Problem-Solving Strategies	42	(2)
Straightedge and Compass Constructions	44	(13)
Chapter Summary	50	(1)
Chapter Review	51	(2)
Chapter Checkup	53	(1)
Reasoning
Chapter Overview	54	(2)
Chapter Exploration: Making Conjectures Using Inductive Reasoning	56	(1)
Exploring Patterns	57	(7)
Using a Computer Drawing Program: Exploring Angle Measure	63	(1)
The Structure of Geometry	64	(7)
Mixed Review: Algebra and Geometry	70	(1)
Milestones: Early Geometry	70	(1)
Segment and Angle Relationships	71	(7)
Mid-Chapter Self-Test	77	(1)
Conditional Statements	78	(6)
Mixed Review: Algebra and Geometry	83	(1)
Reasoning with Properties from Algebra	84	(6)
Deductive Reasoning	90	(15)
Chapter Summary	96	(1)
Chapter Review	97	(4)
Chapter Test	101	(1)
Lines in a Plane
Chapter Overview	102	(2)
Chapter Exploration: Making Conjectures about Lines in the Plane	104	(1)
Exploring Lines and Planes	105	(6)
Connections to Algebra	111	(9)
Mixed Review: Algebra and Geometry	117	(1)
Career Interview: Physical Education Instructor	117	(1)
Special Project: Line Designs	118	(2)
Using the Laws of Logic	120	(6)
Styles of Proofs	126	(8)
Mid-Chapter Self-Test	133	(1)
Properties of Parallel Lines	134	(7)
Using a Computer Drawing Program: Exploring Parallel Lines	140	(1)
Proving Lines Are Parallel	141	(6)
Mixed Review: Algebra and Geometry	146	(1)
Extended Application: Vectors	147	(16)
Chapter Summary	153	(1)
Chapter Review	154	(3)
Chapter Test	157	(1)
Cumulative Review for Chapters 1-3	158	(2)
Congruent Triangles
Chapter Overview	160	(2)
Chapter Exploration: Making Conjectures about Congruent Triangles	162	(1)
Exploring Congruent Triangles	163	(6)
Angles of a Triangle	169	(8)
Mixed Review: Algebra and Geometry	175	(1)
Milestones: Golden Age of Greece	175	(1)
Using a Computer Drawing Program: Exploring Congruent Triangles	176	(1)
Proving that Triangles Are Congruent	177	(6)
More Ways to Prove that Triangles Are Congruent	183	(7)
Mid-Chapter Self-Test	189	(1)
Using Congruent Triangles	190	(12)
Isosceles Triangles and Right Triangles	196	(5)
Mixed Review: Algebra and Geometry	201	(1)
Extended Application: Constructions	202	(15)
Chapter Summary	208	(1)
Chapter Review	209	(4)
Chapter Test	213	(1)
Properties of Triangles
Chapter Overview	214	(2)
Chapter Exploration: Making Conjectures Using Taxi Geometry	216	(1)
Exploring Parts of Triangles	217	(7)
Special Segments in a Triangle	224	(8)
Mixed Review: Algebra and Geometry	230	(1)
Career Interview: Fashion Designer	230	(1)
Using a Graphing Calculator: Exploring Centroids	231	(1)
Midsegment Theorem	232	(8)
Mid-Chapter Self-Test	239	(1)
Inequalities in One Triangle	240	(6)
Inequalities in Two Triangles	246	(6)
Mixed Review: Algebra and Geometry	251	(1)
Extended Application: Constructions	252	(15)
Chapter Summary	258	(1)
Chapter Review	259	(4)
Chapter Test	263	(1)
Polygons
Chapter Overview	264	(2)
Chapter Exploration: Making Conjectures about Polygons	266	(1)
Exploring Polygons	267	(6)
Angles of Polygons	273	(7)
Mixed Review: Algebra and Geometry	279	(1)
Milestones: Projective Geometry	279	(1)
Properties of Parallelograms	280	(7)
Mid-Chapter Self-Test	286	(1)
Proving Quadrilaterals Are Parallelograms	287	(6)
Special Parallelograms	293	(6)
Mixed Review: Algebra and Geometry	298	(1)
Trapezoids	299	(7)
Using a Computer Drawing Program: Exploring Polygons	305	(1)
Extended Application: Congruence and Kites	306	(19)
Chapter Summary	312	(1)
Chapter Review	313	(4)
Chapter Test	317	(1)
Cumulative Review for Chapters 1-6	318	(4)
Transformations: Revisiting Congruence
Chapter Overview	322	(2)
Chapter Exploration: Making Conjectures about Motion in a Plane	324	(1)
Exploring Rigid Motion in a Plane	325	(6)
Reflections	331	(7)
Mixed Review: Algebra and Geometry	337	(1)
Career Interview: Cabinetmaker	337	(1)
Rotations	338	(7)
Mid-Chapter Self-Test	344	(1)
Translations	345	(6)
Glide Reflections and Compositions	351	(7)
Mixed Review: Algebra and Geometry	356	(1)
Using a Computer Drawing Program: Exploring Transformations	357	(1)
Extended Application: Frieze Patterns	358	(15)
Chapter Summary	364	(1)
Chapter Review	365	(4)
Chapter Test	369	(1)
Similarity
Chapter Overview	370	(2)
Chapter Exploration: Making Conjectures about Similarity	372	(1)
Exploring Ratio and Proportion	373	(6)
Problem Solving with Proportions	379	(8)
Mixed Review: Algebra and Geometry	385	(1)
Milestones: Analytic Geometry	385	(1)
Using a Computer Drawing Program: Exploring Similarity	386	(1)
Similar Polygons	387	(7)
Mid-Chapter Self-Test	393	(1)
Similar Triangles	394	(6)
Proving that Triangles Are Similar	400	(6)
Proportions in Similar Triangles	406	(6)
Mixed Review: Algebra and Geometry	411	(1)
Extended Application: Dilations	412	(15)
Chapter Summary	418	(1)
Chapter Review	419	(4)
Chapter Test	423	(1)
Right Triangles
Chapter Overview	424	(2)
Chapter Exploration: Making Conjectures about Right Triangles	426	(1)
Exploring Right Triangles	427	(7)
Using a Computer Drawing Program: Exploring Right Triangles	433	(1)
The Pythagorean Theorem	434	(7)
Mixed Review: Algebra and Geometry	440	(1)
Career Interview: Newspaper Reporter	440	(1)
The Converse of the Pythagorean Theorem	441	(7)
Mid-Chapter Self-Test	447	(1)
Special Right Triangles	448	(6)
Trigonometric Ratios	454	(8)
Mixed Review: Algebra and Geometry	459	(1)
Special Project: Indirect Measurement	460	(2)
Extended Application: Solving Right Triangles	462	(17)
Chapter Summary	468	(1)
Chapter Review	469	(4)
Chapter Test	473	(1)
Cumulative Review for Chapters 7-9	474	(2)
Circles
Chapter Overview	476	(2)
Chapter Exploration: Making Conjectures about Circles	478	(1)
Exploring Circles	479	(6)
Properties of Tangents	485	(7)
Mixed Review: Algebra and Geometry	491	(1)
Milestones: Non-Euclidean Geometry	491	(1)
Central Angles and Arcs	492	(7)
Mid-Chapter Self-Test	498	(1)
Arcs and Chords	499	(6)
Inscribed Angles	505	(6)
Mixed Review: Algebra and Geometry	510	(1)
Other Angle Relationships	511	(7)
Using a Computer Drawing Program: Exploring Segment Lengths	517	(1)
Extended Application: Equations of Circles	518	(15)
Chapter Summary	524	(1)
Chapter Review	525	(4)
Chapter Test	529	(1)
Planar Measurements
Chapter Overview	530	(2)
Chapter Exploration: Making Conjectures about Perimeter and Area	532	(1)
Exploring Area and Perimeter	533	(6)
Areas of Parallelograms and Triangles	539	(7)
Mixed Review: Algebra and Geometry	545	(1)
Career Interview: Astronomy Writer	545	(1)
Areas of Other Quadrilaterals	546	(7)
Mid-Chapter Self Test	552	(1)
Areas of Regular Polygons	553	(7)
Using a Scientific Calculator: Exploring Perimeter	559	(1)
Circumference and Arc Length of Circles	560	(6)
Mixed Review: Algebra and Geometry	565	(1)
Areas of Circles and of Regions of Circles	566	(6)
Extended Application: Areas of Similar Polygons	572	(15)
Chapter Summary	578	(1)
Chapter Review	579	(4)
Chapter Test	583	(1)
Space Measurements
Chapter Overview	584	(2)
Chapter Exploration: Making Conjectures about Space Measurements	586	(1)
Exploring Solids	587	(6)
Surface Area of Prisms and Cylinders	593	(7)
Mixed Review: Algebra and Geometry	599	(1)
Milestones: Fractal Geometry	599	(1)
Surface Area of Pyramids and Cones	600	(7)
Mid-Chapter Self-Test	606	(1)
Volume of Prisms and Cylinders	607	(7)
Using a Computer Spreadsheet: Exploring Surface Area	613	(1)
Volume of Pyramids and Cones	614	(6)
Mixed Review: Algebra and Geometry	619	(1)
Surface Area and Volume of Spheres	620	(6)
Extended Application: Similar Solids	626	(19)
Chapter Summary	632	(1)
Chapter Review	633	(4)
Chapter Test	637	(1)
Cumulative Review for Chapters 7-12	638	(4)
Loci
Chapter Overview	642	(2)
Chapter Exploration: Making Conjectures about Loci	644	(1)
Exploring Loci in a Plane	645	(6)
Exploring Loci in Space	651	(7)
Mixed Review: Algebra and Geometry	657	(1)
Career Interview: Human Services Manager	657	(1)
Loci and Problem Solving	658	(7)
Mid-Chapter Self-Test	664	(1)
Loci and Mathematical Models	665	(7)
Using a Graphing Calculator: Loci	671	(1)
Loci and Cross Sections	672	(6)
Mixed Review: Algebra and Geometry	677	(1)
The Bigger Picture of Geometry	678	(14)
Chapter Summary	684	(1)
Chapter Review	685	(4)
Chapter Test	689	(1)
Excursions in Geometry
Overview	690	(2)
Tilings in a Plane	692	(6)
Platonic and Archimedean Solids	698	(6)
Topology and Mobius Strips	704	(6)
Topology and Networks	710	(6)
Spherical Geometry	716	(6)
Fractal Geometry	722	(6)
Projective Geometry	728	(7)
Student Handbook
Symbols	735	(1)
Properties of Real Numbers	736	(1)
Postulates and Theorems	737	(8)
Glossary	745	(12)
Formulas	757	(2)
Table of Squares and Square Roots	759	(1)
Table of Trigonometric Ratios	760	(2)
Algebra Reference	762	(23)
Hints for Selected Proof Exercises	785	(6)
Appendix 1: A Brief History of Geometry	791	(2)
Appendix 2: Coordinate Geometry Investigations	793	(2)
Selected Answers	795	(61)
Index	856
Technology Update	1