D is a point on side QR of ΔPQR

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:

False

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]

Leave a comment

Close

Click here to get exam-ready with eSaral

For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.

Download Now