# Plane Geometry

Century Company, 1916 - Geometry, Modern - 276 pages
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### Contents

 LIST OF SYMBOLS FACING PAGE 1 1183 83 112146 112 147167 147
 168220 168 221269 221 APPENDIX SOME GEOMETRICAL PARADOXES 270273 270 Copyright

### Popular passages

Page 33 - If two triangles have two sides of the 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. Hyp. In A ABC and A'B'C' AB = A'B'; AC = A'C'; ZA>ZA'.
Page 189 - The areas of two triangles which have 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. D c A' D' Hyp. In triangles ABC and A'B'C', ZA = ZA'. To prove AABC = ABxAC. A A'B'C' A'B'xA'C' Proof. Draw the altitudes BD and B'D'.
Page 72 - The line joining the midpoints of two sides of a triangle is parallel to the third side and equal to one-half of it.
Page 82 - If two triangles have two sides of the one respectively equal to two sides of the other, and the contained angles supplemental, the two triangles are equal.
Page 40 - Euclid, eg first asserts and proves, that the exterior angle of a triangle is greater than either of the interior opposite angles...
Page 107 - 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 diminished by twice the product of one of those sides and the projection of the other upon that side.
Page 189 - ... 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 133 - The sum of the angles of a triangle is equal to a straight angle.
Page 166 - The locus of a point at a given distance from a given point is the circumference described from the point with the
Page 78 - The lines joining the mid-points of the opposite sides of a quadrilateral bisect each other.