Question

How to prove a paralelllogram is rectangle if the diagonals are equal

Answer 1

lets us consider, ABCD is a parallelogram

Given –
the diagonals AC and BD of parallelogram ABCD are equal .

Now,

In ∆ ABD and ∆ACD.

AC = BD [Given]

AB = DC [opposite sides of a parallelogram]

AD = AD [Common side]

∴ ΔABD ≅ ΔDCA [SSS congruence criterion]

∠BAD = ∠CDA [CPCT]

∠BAD + ∠CDA = 180° [Adjacent angles of a parallelogram are supplementary.]

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

Therefore, parallelogram ABCD is a rectangle since a parallelogram with one right interior angle is a rectangle.
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