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Question
A parallelogram PQRS is constructed with sides QR = 6 cm, PQ = 4 cm and ∠PQR = 90°. Then PQRS is a ______.
Options
square
rectangle
rhombus
trapezium
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Solution
A parallelogram PQRS is constructed with sides QR = 6 cm, PQ = 4 cm and ∠PQR = 90°. Then PQRS is a rectangle.
Explanation:
Given PQRS is a parallelogram such that PQ = 4 cm, QR = 6 cm and ∠PQR = 90°
∠PQR + ∠SRQ = 180° ...[∵ Sum of interior angles on same side of transversal is 180°]
`\implies` ∠SRQ = 90°
Similarly, all the interior angles are 90°.
Hence, PQRS is a rectangle.
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