# Plane Geometry

B.H. Sanborn & Company, 1916 - Geometry - 278 pages
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### Contents

 OHAPTER PAGE I FUNDAMENTAL IDEAS 1 PARALLEL AND PERPENDICULAR LINES 24 PROOF BY SUPERPOSITION 46 POLYGONS 65 CONCURRENT LINES 84 SIMILAR POLYGONS 94
 METHODS OF ATTACK 130 CIRCLES 146 NUMERICAL RELATIONS 190 AREAS OF POLYGONS 213 REGULAR POLYGONS AND CIRCLES 237 Copyright

### Popular passages

Page 130 - If two triangles have two sides of one equal respectively to two sides of the other, but the included angle of the first greater than the included angle of the second, then the third side of the first is greater than the third side of the second.
Page 76 - The straight line joining the middle points of two sides of a triangle is parallel to the third side and equal to half of it 46 INTERCEPTS BY PARALLEL LINES.
Page 223 - ... they have an angle of one equal to an angle of the other and the including sides are proportional; (c) their sides are respectively proportional.
Page 4 - PERIPHERY of a circle is its entire bounding line ; or it is a curved line, all points of which are equally distant from a point within called the center.
Page 21 - If the first of three quantities is greater than the second, and the second is greater than the third, then the first is greater than the third.
Page 222 - Two triangles having an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles.
Page 131 - ... if two triangles have two sides of one equal, respectively, to two sides of the other...
Page 72 - There are three important theorems in geometry stating the conditions under which two triangles are congruent: 1. Two triangles are congruent if two sides and the included angle of one are equal respectively to two sides and the included angle of the other.
Page 258 - 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 197 - In any triangle, the square of the side opposite an acute angle is equal to the sum of the squares of the other two sides, minus twice the product of one of these sides and the projection of the other side upon it.