# The Essentials of Geometry (plane)

D.C. Heath & Company, 1898 - 242 pages
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### Popular passages

Page 49 - ... the three sides of one are equal, respectively, to the three sides of the other. 2. Two right triangles are congruent if...
Page 124 - In any proportion the terms are in proportion by Composition ; that is, the sum of the first two terms is to the first term as the sum of the last two terms is to the third term.
Page 151 - If one leg of a right triangle is double the other, the perpendicular from the vertex of the right angle to the hypotenuse divides it into segments which are to each other as 1 to 4.
Page 40 - 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 192 - The perimeters of two regular polygons of the same number of sides, are to each other as their homologous sides, and their areas are to each other as the squares of those sides (Prop.
Page 124 - In any proportion the terms are in proportion by Alternation ; that is, the first term is to the third as the second term is to the fourth.
Page 138 - If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar.
Page 224 - The perpendiculars from the vertices of a triangle to the opposite sides are the bisectors of the angles of the triangle formed by joining the feet of the perpendiculars.
Page 58 - 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.
Page 49 - If the opposite sides of a quadrilateral are equal, the figure is a parallelogram.