Beman, Wooster Woodruff, 1850-1922, Smith, David Eugene, 1860-1944 · Boston, Ginn & company · leaf 125
108 PLANE GEOMETRY. [Bk. II. Proposition XI. 161. Theorem. The sum of the squares on the sides of aquadrilateral equals the sum of the squares on the diagonalsplus four times the square on the line joining the mid-pointsof the diagonals. Pr … Given a quadrilateral abed, convex, concave, or cross, withdiagonals e, f and with m joining the mid-pointsof e, f. To prove that a2 + b2 + c2 + d2 = e2 + f2 + 4 m2. Proof. 1. In the figure, a2 + d2 = 2 x2 + 2 I % J , Why ? •GO- ? 00 ? and b2 + c2 = 2y2 + 2 (% • Why? 2. .. a2 + 62 + c2 + d2 = 2 (x2…
Geometry
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