Plane Geometry

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

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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.

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