Informal Geometry

by Merrill

• ISBN13: 9780675058544
• ISBN10: 0675058546
• Format: Hardcover
• Copyright: 1988-01-01
• Publisher: Glencoe/McGraw-Hill School Pub

Table of Contents

An Introduction to Informal Geometry
Drawings in Geometry---Optical Illusions	3	(4)
Points, Lines, and Planes	7	(6)
Tools of the Trade	13	(5)
Postulates	18	(3)
Conditional Statements and Their Converses	21	(5)
An Introduction to Logo	26	(7)
Segment Measure
Number Lines	33	(5)
Measuring	38	(4)
Segments and the Properties of Real Numbers	42	(3)
Congruent Segments	45	(4)
Segments and Inequalities	49	(4)
An Introduction to Perimeter	53	(8)
Angle Measure
Angles	61	(3)
Angle Measure	64	(5)
The Angle Addition Postulate	69	(5)
Pairs of Angles	74	(5)
Congruent Angles	79	(4)
Perpendicular Lines	83	(10)
Triangles
Classifying Triangles	93	(4)
Angle Measures	97	(4)
Congruence	101	(4)
SSS and SAS Congruence Postulates	105	(6)
ASA Congruence Postulate and AAS Theorem	111	(4)
Proving Triangles Congruent	115	(8)
More About Triangles
Medians	123	(4)
Altitudes and Perpendicular Bisectors	127	(5)
Angle Bisectors of Triangles	132	(3)
Isosceles Triangles	135	(3)
More About Isosceles Triangles	138	(4)
Right Triangles	142	(11)
Triangle Inequalities
The Exterior Angle Theorem	153	(6)
Inequalities Within a Triangle	159	(5)
The Triangle Inequality Theorem	164	(5)
The Hinge Theorem	169	(8)
Parallels
Parallel Lines and Planes	177	(3)
Parallels and Interior Angles	180	(4)
Parallel Lines and Corresponding Angles	184	(4)
When Are Lines Parallel?	188	(5)
Using Parallel Lines	193	(10)
Quadrilaterals
Introduction to Quadrilaterals	203	(4)
Types of Quadrilaterals	207	(4)
Properties of Parallelograms	211	(5)
Tests for Parallelograms	216	(4)
Rectangles, Rhombuses, and Squares	220	(5)
Properties of Trapezoids	225	(5)
Perimeter and Symmetry in Quadrilaterals	230	(9)
Similarity
Ratio and Proportion	239	(4)
Applications of Proportions	243	(4)
Similar Polygons	247	(4)
Similar Triangles	251	(6)
Proportional Parts and Triangles	257	(3)
Proportional Parts and Parallel Lines	260	(7)
Applications of Similar Triangles
Perimeters and Similarity	267	(4)
Altitudes and Similarity	271	(4)
Angle Bisectors and Similarity	275	(4)
Medians and Similarity	279	(3)
The Golden Rectangle	282	(2)
Using Similar Triangles	284	(9)
Polygons and Area
Naming Polygons	293	(3)
Diagonals and Angle Measures of Polygons	296	(6)
Area of Polygonal Regions	302	(4)
Area of Rectangles and Triangles	306	(5)
Area of Parallelograms	311	(6)
Area of Trapezoids	317	(4)
Area of Regular Polygons	321	(6)
Right Triangles
Squares and Square Roots	327	(3)
Computing with Square Roots	330	(4)
The Pythagorean Theorem	334	(5)
Using the Pythagorean Theorem	339	(3)
Special Right Triangles	342	(6)
The Geometric Mean-Similar Right Triangles	348	(9)
Circles and Area
Parts of a Circle	357	(4)
Arcs and Angles	361	(4)
Arcs and Chords	365	(5)
Inscribed Polygons	370	(4)
Circumference of a Circle	374	(5)
Area of a Circle	379	(8)
Circle Relationships
Inscribed Angles	387	(5)
Tangents to a Circle	392	(4)
Secant Angles	396	(4)
Secant-Tangent Angles	400	(5)
Segment Lengths	405	(10)
Surface Area and Volume
Polyhedrons and Prisms	415	(4)
Surface Area of Prisms and Cylinders	419	(5)
Volume of Prisms and Cylinders	424	(4)
Surface Area of Pyramids and Cones	428	(4)
Volume of Pyramids and Cones	432	(4)
Spheres	436	(7)
Coordinate Geometry
The Coordinate Plane	443	(3)
Distances and Midpoints	446	(4)
Slope	450	(4)
Equations for a Line	454	(5)
Systems of Equations	459	(5)
Equations of Circles	464	(9)
Motion Geometry--Transformations
Geometry in Motion	473	(3)
Flips--Reflections	476	(4)
Slides--Translations	480	(4)
Turns--Rotations	484	(6)
Tessellations	490	(7)
Trigonometry
Sine	497	(3)
Cosine	500	(4)
Tangent	504	(3)
Using the Trigonometric Table	507	(4)
Applications of Trigonometric Ratios	511	(3)
Using Trigonometry in Logo	514	(6)
Table of Square Roots	520	(1)
Table of Trigonometric Ratios	521	(1)
Postulates and Theorems	522	(11)
Glossary	533	(8)
Selected Answers	541	(16)
Index	557