Question

ABCD is a parallelogram. If two diagonals are equal, then prove that ABCD is a rectangle.

Answer 1

$\huge\bf\blue{Hey\:Mate!!!}$

Given : A parallelogram ABCD , in which AC = BD

To Prove : ABCD is a rectangle .

Proof : In △ABC and △ABD

AB = AB (common)

AC = BD (given)

BC = AD (opp . sides of a parallelogram)

⇒ △ABC ≅ △BAD (by SSS congruency)

⇒ ∠ABC = △BAD (By CPCT)

Also, ∠ABC + ∠BAD = 180° (co - interior angles)

⇒ ∠ABC + ∠ABC = 180° (∵ ∠ABC = ∠BAD)

⇒ 2∠ABC = 180°

⇒ ∠ABC = 1 /2 × 180° = 90°

Hence, parallelogram ABCD is a rectangle.

@ItsMysteriousGirl✒️

Answer 2

Answer:

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