# Plane Geometry

American Book Company, 1911 - Geometry, Modern - 303 pages

### Contents

 Lines 1 Demonstrations 13 RECTILINEAR FIGURES 19 Superposition 25 Measurement of Distances by Means of Triangles 32 Summary of Equal Triangle Theorems 42 Summary of Unequal Angle Theorems 65 Summary of Parallel Line Theorems 84
 Construction of Triangles 106 THE CIRCLE 113 vi 122 BOOK III 161 AREAS OF POLYGONS 209 REGULAR POLYGONS MEASUREMENT OF 245 APPENDIX TO PLANE GEOMETRY 284 INDEX 291

 Concurrent Line Theorems 100
 PAGE 297

### Popular passages

Page 281 - The bisector of an angle of a triangle divides the opposite side into segments proportional to the adjacent sides.
Page 268 - S' denote the areas of two circles, R and R' their radii, and D and D' their diameters. Then, I . 5*1 = =»!. That is, the areas of two circles are to each other as the squares of their radii, or as the squares of their diameters.
Page 76 - If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I.
Page 179 - For, if we have given ab' = a'b, then, dividing by bb', we obtain Corollary. The terms of a proportion may be written In any order which will make the product of the extremes equal to the product of the means.
Page 95 - The line joining the mid-points of two sides of a triangle is parallel to the third side, and equal to half the third side.
Page 195 - The square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of the other two sides. 3. In a right triangle the square of either leg is equal to the square of the hypotenuse minus the square of the other leg.
Page 13 - If two angles of a triangle are equal, the sides opposite are equal.
Page 96 - A line joining the midpoints of the non.parallel sides of a trapezoid is parallel to the base, and equal to half the sum of the bases.
Page 64 - ... if two triangles have two sides of one equal, respectively, to two sides of the other...
Page 94 - If three or more parallel lines intercept equal segments on one transversal, they intercept equal segments on any other transversal.