In parallelogram ABCD, the diagonals are equal. Prove that ABCD is a rectangle.
| September 5, 2021 | education
Since, according to the condition, BD = AC, and the opposite sides of the parallelogram are equal, BC = AD, AB = CD, the triangles ABD and ACD are equal on three sides. Then the angle BAD = CDA. Since the parallelogram has a sum of adjacent angles equal to 180, the angle BAD + CDA = 180.
2 * BAD = 180.
The angle BAD = CDA = 180/2 = 90, therefore, ABCD is a rectangle, which is what was required to be proved.
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