Question

D is a point on side QR of ΔPQR such that PD ⊥ QR. Will it be correct to say that ΔPQD ~ ΔRPD? Why?

Answer 1

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]