Math, asked by dikshantsaini37, 4 months ago

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

Answers

Answered by Anonymous
1

Answer:

Sorry I don`t know the answer,

but pls give me brainliest!

Step-by-step explanation:

Answered by prachirathod2007
1

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 | | gm]

⇒ △ABC ≅ △BAD [ by SSS congruence axiom]

⇒ ∠ABC = △BAD [c.p.c.t.]

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.

hope this may help

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