Geometry

by Jergensen, Brown; Brown, Richard G.; Jurgensen, John W.

• ISBN13: 9780395771204
• ISBN10: 039577120X
• Format: Hardcover
• Copyright: 1996-03-01
• Publisher: McDougal Littell/Houghton Mifflin

Table of Contents

Points, Lines, Planes, and Angles
Some Basic Figures
A Game and Some Geometry	1	(4)
Points, Lines, and Planes	5	(6)
Definitions and Postulates
Segments, Rays, and Distance	11	(6)
Angles	17	(5)
Postulates and Theorems Relating Points, Lines, and Planes	22	(11)
Deductive Reasoning
Using Deductive Reasoning
If-Then Statements; Converses	33	(4)
Properties from Algebra	37	(6)
Proving Theorems	43	(7)
Theorems about Angles and Perpendicular Lines
Special Pairs of Angles	50	(6)
Perpendicular Lines	56	(4)
Planning a Proof	60	(13)
Parallel Lines and Planes
When Lines and Planes Are Parallel
Defintions	73	(5)
Properties of Parallel Lines	78	(5)
Proving Lines Prallel	83	(10)
Applying Prallel Lines to Polygons
Angles of a Triangle	93	(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 Traingles 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 Traingles
A Postulate for Similar Triangles	254	(9)
Theorems for Similar Triangles	263	(6)
Proportional Lengths	269	(16)
Right Triangles
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