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2. If the diagonals of a parallelogram are equal, then showthat it is a rectangle.

Harshit Singh , 3 Years ago
Grade 12th pass
anser 1 Answers
Pawan Prajapati

Last Activity: 3 Years ago

Consider triangles DAB and CBA, AD = BC [Opposite sides of a parallelogram] AB is common. AC = BD :. Ii DAB ::Ii CBA => L DAB = L CBA [Given] [ss.sJ DC A B ••.(i) [CPCT) As ABCD is a parallelogram. AD II BC and AB is transversal. .. L DAB + L CBA = 180° [Sum of interior angles on the same side of transversal is 180°.) => 2L DAB = 180° [From (i)] => L DAB = 90° As in a parallelogram, LDAB = 90°. Hence, the parallelogram is a rectangle.

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