Geometry

by Larson, Ron; Boswell, Laurie; Stiff, Lee

• ISBN13: 9780669316650
• ISBN10: 0669316652
• Format: Hardcover
• Copyright: 1995-01-01
• Publisher: HOUGHTON MIFFLIN COMPANY (TRADE DIVISION)

Table of Contents

An Overview of Geometry
Chapter Overview	1	(1)
What is Geometry?	2	(1)
Exploring Optical Illusions A, C	3	(6)
Exploring Shapes A,C	9	(7)
Mixed Review: Algebra and Geometry	15	(1)
Career Interview: Commercial Pilot	15	(1)
Exploring Congruence and Similarity C,F	16	(6)
Exploring Symmetry A,C	22	(8)
Using a Computer Drawing Program: Exploring Congruence and Similarity	28	(1)
Mid-Chapter Partner Quiz	29	(1)
Coordinate Geometry and Noncoordinate Geometry A,C,D	30	(6)
Exploring Measure A,C,F	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 A,C	51	(2)
Chapter Checkup	53	(1)
Reasoning
Chapter Overview	54	(2)
Chapter Exploration: Making Conjectures Using Inductive Reasoning	56	(1)
Exploring Patterns A,C,F	57	(7)
Using a Computer Drawing Program: Exploring Angle Measure	63	(1)
The Structure of Geometry A,D	64	(7)
Mixed Review: Algebra and Geometry	70	(1)
Milestones: Early Geometry	70	(1)
Segment and Angle Relationships c	71	(7)
Mid-Chapter Self-Test	77	(1)
Conditional Statements A	78	(6)
Mixed Review: Algebra and Geometry	83	(1)
Reasoning with Properties from Algebra A,D	84	(6)
Deductive Reasoning A,C	90	(15)
Chapter Summary	96	(1)
Chapter Review C,D	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 C,F	105	(6)
Connections to Algebra A,C	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 D	120	(6)
Styles of Proofs C,D	126	(8)
Mid-Chapter Self-Test	133	(1)
Properties of Parallel Lines A,C	134	(7)
Using a Computer Drawing Program: Exploring Parallel Lines	140	(1)
Proving Lines Are Parallel A,D	141	(6)
Mixed Review: Algebra and Geometry	146	(1)
Extended Application: Vectors C,F	147	(16)
Chapter Summary	153	(1)
Chapter Review D	154	(3)
Chapter Test	157	(1)
Cumulative Review for Chapters 1--3 D	158	(2)
Congruent Triangles
Chapter Overview	160	(2)
Chapter Exploration: Making Conjectures about Congruent Triangles	162	(1)
Exploring Congruent Triangles A,C,D	163	(6)
Angles of a Triangle A,D	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 C,F	177	(6)
More Ways to Prove that Triangles Are Congruent A,C	183	(7)
Mid-Chapter Self-Test	189	(1)
Using Congruent Triangles D	190	(6)
Isosceles Triangles and Right Triangles A,F	196	(6)
Mixed Review: Algebra and Geometry	201	(1)
Extended Application: Constructions	202	(15)
Chapter Summary	208	(1)
Chapter Review D,F	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 A,C	217	(7)
Special Segments in a Triangle A,C	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 A,C,D,F	232	(8)
Mid-Chapter Self-Test	239	(1)
Inequalities in One Triangle A,C,D	240	(6)
Inequalities in Two Triangles A,D	246	(6)
Mixed Review: Algebra and Geometry	251	(1)
Extended Application: Constructions A,C	252	(15)
Chapter Summary	258	(1)
Chapter Review C	259	(4)
Chapter Test	263	(1)
Polygons
Chapter Overview	264	(2)
Chapter Exploration: Making Conjectures about Polygons	266	(1)
Exploring Polygons D,F	267	(6)
Angles of Polygons A,C,F	273	(7)
Mixed Review: Algebra and Geometry	279	(1)
Milestones: Projective Geometry	279	(1)
Properties of Parallelograms A,C,D	280	(7)
Mid-Chapter Self-Test	286	(1)
Proving Quadrilaterals Are Parallelograms A,C	287	(6)
Special Parallelograms A,C	293	(6)
Mixed Review: Algebra and Geometry	298	(1)
Trapezoids C,D	299	(7)
Using a Computer Drawing Program: Exploring Polygons	305	(1)
Extended Application: Congruence and Kites A,C,D	306	(19)
Chapter Summary	312	(1)
Chapter Review D,F	313	(4)
Chapter Test	317	(1)
Cumulative Review for Chapters 1--6 A,D	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 C,F	325	(6)
Reflections A,C	331	(7)
Mixed Review: Algebra and Geometry	337	(1)
Career Interview: Cabinetmaker	337	(1)
Rotations C,D	338	(7)
Mid-Chapter Self-Test	344	(1)
Translations C	345	(6)
Glide Reflections and Compositions A,C	351	(7)
Mixed Review: Algebra and Geometry	356	(1)
Using a Computer Drawing Program: Exploring Transformations	357	(1)
Extended Application: Frieze Patterns D,F	358	(15)
Chapter Summary	364	(1)
Chapter Review C,F	365	(4)
Chapter Test	369	(1)
Similarity
Chapter Overview	370	(2)
Chapter Exploration: Making Conjectures about Similarity	372	(1)
Exploring Ratio and Proportion A,D,F	373	(6)
Problem Solving with Proportions A,D	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 A,F	387	(7)
Mid-Chapter Self-Test	393	(1)
Similar Triangles A,C	394	(6)
Proving that Triangles Are Similar A,F	400	(6)
Proportions in Similar Triangles A,F	406	(6)
Mixed Review: Algebra and Geometry	411	(1)
Extended Application: Dilations C	412	(15)
Chapter Summary	418	(1)
Chapter Review A	419	(4)
Chapter Test	423	(1)
Right Triangles
Chapter Overview	424	(2)
Chapter Exploration: Making Conjectures about Right Triangles	426	(1)
Exploring Right Triangles A	427	(7)
Using a Computer Drawing Program: Exploring Right Triangles	433	(1)
The Pythagorean Theorem A,C,F	434	(7)
Mixed Review: Algebra and Geometry	440	(1)
Career Interview: Newspaper Reporter	440	(1)
The Converse of the Pythagorean Theorem A,C,D	441	(7)
Mid-Chapter Self-Test	447	(1)
Special Right Triangles A,F	448	(6)
Trigonometric Ratios A,F	454	(8)
Mixed Review: Algebra and Geometry	459	(1)
Special Project: Indirect Measurement	460	(2)
Extended Application: Solving Right Triangles D	462	(17)
Chapter Summary	468	(1)
Chapter Review A	469	(4)
Chapter Test	473	(1)
Cumulative Review for Chapters 7--9 A	474	(2)
Circles
Chapter Overview	476	(2)
Chapter Exploration: Making Conjectures about Circles	478	(1)
Exploring Circles	479	(6)
Properties of Tangents A,D	485	(7)
Mixed Review: Algebra and Geometry	491	(1)
Milestones: Non-Euclidean Geometry	491	(1)
Central Angles and Arcs A,C,D	492	(7)
Mid-Chapter Self-Test	498	(1)
Arcs and Chords C,D	499	(6)
Inscribed Angles A,D	505	(6)
Mixed Review: Algebra and Geometry	510	(1)
Other Angle Relationships A	511	(7)
Using a Computer Drawing Program: Exploring Segment Lengths	517	(1)
Extended Application: Equations of Circles A,C	518	(15)
Chapter Summary	524	(1)
Chapter Review A,C	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 A,C,F	533	(6)
Areas of Parallelograms and Triangles A,C,D,F	539	(7)
Mixed Review: Algebra and Geometry	545	(1)
Career Interview: Astronomy Writer	545	(1)
Areas of Other Quadrilaterals C,D	546	(7)
Mid-Chapter Self Test	552	(1)
Areas of Regular Polygons C	553	(7)
Using a Scientific Calculator: Exploring Perimeter	559	(1)
Circumference and Arc Length of Circles A,D	560	(6)
Mixed Review: Algebra and Geometry	565	(1)
Areas of Circles and of Regions of Circles F	566	(6)
Extended Application: Areas of Similar Polygons A,F	572	(15)
Chapter Summary	578	(1)
Chapter Review D	579	(4)
Chapter Test	583	(1)
Space Measurements
Chapter Overview	584	(2)
Chapter Exploration: Making Conjectures about Space Measurements	586	(1)
Exploring Solids C,D	587	(6)
Surface Area of Prisms and Cylinders A,D	593	(7)
Mixed Review: Algebra and Geometry	599	(1)
Milestones: Fractal Geometry	599	(1)
Surface Area of Pyramids and Cones A	600	(7)
Mid-Chapter Self-Test	606	(1)
Volume of Prisms and Cylinders A,D	607	(7)
Using a Computer Spreadsheet: Exploring Surface Area	613	(1)
Volume of Pyramids and Cones A	614	(6)
Mixed Review: Algebra and Geometry	619	(1)
Surface Area and Volume of Spheres A	620	(6)
Extended Application: Similar Solids A	626	(19)
Chapter Summary	632	(1)
Chapter Review A	633	(4)
Chapter Test	637	(1)
Cumulative Review for Chapters 7--12 A	638	(4)
Loci
Chapter Overview	642	(2)
Chapter Exploration: Making Conjectures about Loci	644	(1)
Exploring Loci in a Plane A,C	645	(6)
Exploring Loci in Space A,C,D	651	(7)
Mixed Review: Algebra and Geometry	657	(1)
Career Interview: Human Services Manager	657	(1)
Loci and Problem Solving C,D	658	(7)
Mid-Chapter Self-Test	664	(1)
Loci and Mathematical Models A,C,D	665	(7)
Using a Graphing Calculator: Exploring Loci	671	(1)
Loci and Cross Sections A,C	672	(6)
Mixed Review: Algebra and Geometry	677	(1)
The Bigger Picture of Geometry A,C	678	(14)
Chapter Summary	684	(1)
Chapter Review A,C	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	737	(2)
Theorems	739	(6)
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)
Selected Answers	791	(61)
Index	852
Technology Update	TU 1