26ADa В2 Euclid's approach to geometryВBaCFigure 2.5: Dividing a parallelogram into trianglesTherefore, the triangles are congruent by ASA, and in particular wehave the equalities |AB| = |DC| and |AD| = |BC| between correspondingsides. But these are also the opposite sides of the parallelogram.ExercisesUsing the parallelogram side theorem and ASA, find congruent triangles inFigure 2.6. Hence, show that the diagonals of a parallelogram bisect eachother.Figure 2.6: A parallelogram and its diagonalsDeduce that the diagonals of a rhombus-a parallelogram whose sides areall equal-meet at right angles. (Hint: You may find it convenient touse SSS, which says that triangles are congruent when their correspond-ing sides are equal.)Prove the isosceles triangle theorem differently by bisecting the angle at A.

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Elementary Geometry For College Students, 7e

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ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

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Using the parallelogram side theorem and ASA, find congruent triangles in Figure 2.6. Hence, show that the diagonals of a parallelogram bisect each other.