English, asked by Anonymous, 7 months ago

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

Answers

Answered by ItsCuteBaby83
1

Explanation:

Given ▶

A parallelogram PQRS ,in which PR and QS

are diagonals of parallelogram and both are equal

i.e PR = QS

TO prove :PQRS is a rectangle.

Proof ▶∆PQR and ∆ PQS

here ,

PQ = PQ (common )

PR =QS (Given)

QR=PS (opposite sides of parallelogram)

Therefore,

∆PQR ≅∆ PQS (By S.S.S congruency)

⇒ ∠PQR=∠PQS [c.p.c.t.]

Also,

∠PQR+∠PQS = 180°(co- interior angles )

i.e ∠PQR+∠PQR=180°( because ∠PQR=∠PQS proved above )

2 ∠PQR=180°

∠PQR= 90°

Hence , parallelogram PQRS is a rectangle .

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