Mathematics
ABCD is a rhombus with P, Q and R as mid-points of AB, BC and CD respectively. Prove that PQ ⊥ QR.
Mid-point Theorem
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Answer
Join AC and BD.
Diagonals of rhombus intersect at right angle.
∠MON = 90°
In △BCD,
Q and R are mid-points of BC and CD.
RQ || DB and RQ = DB
RQ || DB ⇒ MQ || ON
From figure,
∠MON + ∠MQN = 180° (Sum of alternate angles of quadrilateral = 180°)
∠MQN = 180° - 90° = 90°
∴ PQ ⊥ QR.
Hence, proved that PQ ⊥ QR.
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