# Plane Geometry

Rand McNally & Company, 1918 - Geometry, Modern - 322 pages
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### Contents

 Points and Straight Lines 1 Summary and Supplementary Exercises 15 Tests for Equal Angles and Equal Segments 21 Application of Congruent Triangles to Constructions 30 Miscellaneous Theorems and Exercises 37 Symmetry 48 Angles Made by Parallels and Transversals 54 Angles in Polygons 63
 Maxima and Minima 284 Regular Polygons 290 50 295 Tables 298 59 308 Index 309 66 315 The Preface

 Supplementary Exercises 69 Quadrilaterals 75 Special Quadrilaterals 84 Supplementary Exercises 94 Fundamental Tests of Inequality 100 Supplementary Exercises 106 Introductory 108 Tangents 114 Supplementary Exercises 120 Relation between Inscribed Angles and Their Arcs 126 Relation between Angles Formed by Tangents and Chords 135 Loci 143 Determination of Points by the Intersection of Loci 152 Ratio and Proportion 161 Ratios of Segments Made by Parallels 168 Similar Triangles 176 Important Special Cases 182 Applications of Equal Ratios 191 Summary and Supplementary Exercises 197 30 200 Area and Equivalence 208 Equivalent Polygons 220 Summary and Supplementary Exercises 228 37 231 Similarity 240 Summary and Supplementary Exercises 248 Definition 252 Properties of Regular Polygons 259 48 269 Areas of Circles Sectors and Segments 275
 Parallel Lines and Planes 6 Perpendicular Lines and Planes 12 Perpendiculars and Parallels 18 Proportional Segments 29 Projection 35 Summary and Supplementary Exercises 42 Properties of Polyhedrons Cylinders and Cones 48 Pyramids 60 88 69 The Sphere 76 99 78 105 84 Spherical Angles 86 Supplementary Exercises 102 PAGE 106 The Measurement of Round Bodies in General 125 125 The Measurement of the Cone 129 128 Volumes by Cavalieris Theorem 138 138 V 149 Summary and Supplementary Exercises 156 156 35 160 Similarity and Symmetry 162 Symmetry 172 172 Tables 180 180 42 181 102 196 References and Topics for Mathematics Clubs 202 202 The Index 209 209 Copyright

### Popular passages

Page 87 - The distance between two points on the surface of a sphere is the length of the minor arc of a great circle between them.
Page 300 - Square Measure 144 square inches (sq. in.) = 1 square foot (sq. ft.) 9 square feet = 1 square yard (sq.
Page 193 - The perpendicular bisectors of the sides of a triangle are concurrent at a point which is equally distant from the vertices.
Page 186 - The exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles.
Page 198 - The area of a trapezoid is equal to one-half the product of the altitude and the sum of the bases. THEOREM 116. Two parallelograms or two triangles are equivalent if 1. They have equal bases and are between the same parallels. 2. a = a
Page 180 - LENGTH 12 inches (in.) = 1 foot (ft.) 3 feet = 1 yard (yd.) 5| yards = 1 rod (rd.) 320 rods = 1 mile (mi.) 1 mile = 1,760 yd.
Page 185 - The internal bisector of an angle of a triangle divides the opposite side internally in the ratio of the sides containing the angle, and likewise the external bisector externally.
Page 196 - If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar.
Page 192 - An angle formed by a tangent and a chord is measured by onehalf the intercepted arc.
Page 245 - In a series of equal ratios, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent.