PQRS is a parallelogram, if the two diagonals are equal, then the measure
of PQR is:
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Answer:
90°
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Given : PQRS is a parallelogram
two diagonals are equal
To Find : the measure of angle PQR
Solution:
A parallelogram with equal diagonals is a rectangle
And all angles of a rectangle are right angles
Hence m∠PQR is 90°
Proof:
Compare ΔPQR and ΔQPS
PQ ≅ QP using reflexive property of congruence
QR ≅ PS Opposite sides of parallelogram
PR ≅ QS Given that Diagonals are equal
=> ΔPQR ≅ ΔQPS (SSS congruence)
=> ∠PQR = ∠QPS
Sum of adjacent angles of a parallogram is 180°
=> ∠PQR + ∠QPS = 180°
Hence ∠PQR = ∠QPS = 90°
m∠PQR is 90°
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