Question

if the diagonals of a parallelogram are equal, then show that it is a rectangle.​

Answer 1

Given : ABCD is a parallelogram

consider Δ ACD and Δ ABD

AC = BD (given)

AB = DC (opposite sides of parallelogram)

AD = AD (common side)

∴Δ ACD ≅ Δ ABD (sss test of congruence)

∠ BAD = ∠ CDA

∠BAD + ∠CDA = 180∘ [Adjacent angles of parallelogram are supplementary]

so ∠ BAD and ∠ CDA are right angles as they are congruent and supplementary.

Therefore, ABCD is a rectangle since a

parallelogram with one right interior angle is a rectangle.

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