Geometry: Reteaching and Practice, Manual, Study Guide & Answer Key

by Giarrusso, Jean A.

• ISBN13: 9780395470749
• ISBN10: 0395470749
• Format: Paperback
• Copyright: 1989-10-01
• Publisher: HOUGHTON MIFFLIN CO

Table of Contents

Points, Lines, Planes, and Angles
A Game and Some Geometry	1	(2)
Points, Lines, and Planes	3	(2)
Segments, Rays, and Distance	5	(2)
Angles	7	(2)
Postulates and Theorems Relating Points, Lines, and Planes	9	(2)
Deductive Reasoning
If-Then Statements; Converses	11	(2)
Properties from Algebra	13	(2)
Proving Theorems	15	(2)
Special Pairs of Angles	17	(2)
Perpendicular Lines	19	(2)
Planning a Proof	21	(2)
Parallel Lines and Planes
Definitions	23	(2)
Properties of Parallel Lines, Part 1	25	(2)
Properties of Parallel Lines, Part 2	27	(2)
Proving Lines Parallel, Part 1	29	(2)
Proving Lines Parallel, Part 2	31	(2)
Angles of a Triangle	33	(2)
Angles of a Polygon	35	(2)
Inductive Reasoning	37	(2)
Congruent Triangles
Congruent Figures	39	(2)
Some Ways to Prove Triangles Congruent	41	(2)
Using Congruent Triangles, Part 1	43	(2)
Using Congruent Triangles, Part 2	45	(2)
The Isosceles Triangle Theorems, Part 1	47	(2)
The Isosceles Triangle Theorems, Part 2	49	(2)
Other Methods of Proving Triangles Congruent, Part 1	51	(2)
Other Methods of Proving Triangles Congruent, Part 2	53	(2)
Using More than One Pair of Congruent Triangles	55	(2)
Medians, Altitudes, and Perpendicular Bisectors	57	(2)
Quadrilaterals
Properties of Parallelograms	59	(2)
Ways to Prove that Quadrilaterals Are Parallelograms	61	(2)
Theorems Involving Parallel Lines	63	(2)
Special Parallelograms	65	(2)
Trapezoids	67	(2)
Inequalities in Geometry
Inequalities	69	(2)
Inverses and Contrapositives	71	(2)
Indirect Proof	73	(2)
Inequalities for One Triangle	75	(2)
Inequalities for Two Triangles	77	(2)
Similar Polygons
Ratio and Proportion	79	(2)
Properties of Proportions	81	(2)
Similar Polygons	83	(2)
A Postulate for Similar Triangles	85	(2)
Theorems for Similar Triangles	87	(2)
Proportional Lengths	89	(2)
Right Triangles
Similarity in Right Triangles	91	(2)
The Pythagorean Theorem	93	(2)
The Converse of the Pythagorean Theorem	95	(2)
Special Right Triangles	97	(2)
The Tangent Ratio	99	(2)
The Sine and Cosine Ratios	101	(2)
Applications of Right Triangle Trigonometry	103	(4)
Using a Trigonometric Table	105	(1)
Mixed Trigonometric Exercises	106	(1)
Circles
Basic Terms	107	(2)
Tangents	109	(2)
Arcs and Central Angles	111	(2)
Arcs and Chords	113	(2)
Inscribed Angles	115	(2)
Other Angles	117	(2)
Circles and Lengths of Segments	119	(2)
Constructions and Loci
What Construction Means	121	(2)
Perpendiculars and Parallels	123	(2)
Concurrent Lines	125	(2)
Circles	127	(2)
Special Segments	129	(2)
The Meaning of Locus	131	(2)
Locus Problems	133	(2)
Locus and Construction	135	(2)
Areas of Plane Figures
Areas of Rectangles	137	(2)
Areas of Parallelograms, Triangles, and Rhombuses	139	(2)
Areas of Trapezoids	141	(2)
Areas of Regular Polygons	143	(2)
Circumferences and Areas of Circles	145	(2)
Arc Lengths and Areas of Sectors	147	(2)
Ratios of Areas	149	(2)
Geometric Probability	151	(2)
Areas and Volumes of Solids
Prisms	153	(2)
Pyramids	155	(2)
Cylinders and Cones	157	(2)
Spheres	159	(2)
Areas and Volumes of Similar Solids	161	(2)
Coordinate Geometry
The Distance Formula	163	(2)
Slope of a Line	165	(2)
Parallel and Perpendicular Lines	167	(2)
Vectors	169	(2)
The Midpoint Formula	171	(2)
Graphing Linear Equations	173	(2)
Writing Linear Equations	175	(2)
Organizing Coordinate Proofs	177	(2)
Coordinate Geometry Proofs	179	(2)
Transformations
Mappings and Functions	181	(2)
Reflections	183	(2)
Translations and Glide Reflections	185	(2)
Rotations	187	(2)
Dilations	189	(2)
Composites of Mappings	191	(2)
Inverses and the Identity	193	(2)
Symmetry in the Plane	195	(3)
Symbols	198	(1)
Table of Measures	199	(2)
Table of Squares and Square Roots	201	(1)
Table of Trigonometric Ratios	202