Question

if the diagonals of a parallelogram are equal, prove that it is a rectangle

Answer 1

Given:ABCD is a parallelogram

& AC =BD

To prove: ABCD is a rectangle

Proof: In triangle ABC and ABD

AB=AB (common)

AC=BD (given)

AD=BC (given)

By SSS rule triangle ABC congruent to triangle ABD

Angle A = angle B (by cpct)

Now,

A + B = 180(co-interior angles of parallelogram ABCD)

2A +2B = 180

A + B= 90

So, ABCD is a rectangle

Answer 2

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