Question

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

Answer 1

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Answer 2

HEY FRIEND HERE YOUR ANSWER


lets say, ABCD is a parallelogram


Given that the diagonals AC and BD of parallelogram ABCD are equal in length .


Consider triangles 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.

I HOPE IT'S HELP YOU


MARK BRAINLIEST MY ANSWER ABI

THANKS..........