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