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Question
D is a point on side QR of ΔPQR such that PD ⊥ QR. Will it be correct to say that ΔPQD ~ ΔRPD? Why?
Solution
In ΔPQD and ΔRPD,
PD = PD ...[Common side]
∠PDQ = ∠PDR ...[Each 90°]
Here, no other sides or angles are equal, so we can say that ∠PQD is not similar to ΔRPD.
But, if ∠P = 90°, then ∠DPQ = ∠PRD
[Each equal to 90° – ∠0 and by ASA similarity criterion, ΔPQD ~ΔRPD]
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