D is a point on side QR of △PQR such that PD⟂QR. Will it be correct to say that △PQD ~ △RPD? Why

Solution:

Given, D is a point on the side QR of △PQR.

PD⟂QR

We have to determine if the triangles PQD and RPD are similar.

We know that similar triangles have congruent corresponding angles and the corresponding sides are in proportion.

From the above figure,

PD is the side common to both triangles PQD and RPD.

Since, PD⟂QR we have ∠PDQ = ∠RDP = 90°

Also, PD does not bisect ∠P.

∠QPD ≠ ∠RPD

∠PQD ≠ ∠PRD

This implies that ∠Q ≠ ∠R, so PR ≠ PQ

We observe that the ratio of the corresponding sides are not equal and the corresponding angles are not equal.

Therefore, the triangles PQD and RPD are not similar.

✦ Try This: D is a point on side QR of △PQR such that ∠P = 90°. Will it be correct to say that △PQD ~ △RPD? Why

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 6

NCERT Exemplar Class 10 Maths Exercise 6.2 Problem 10

D is a point on side QR of △PQR such that PD⟂QR. Will it be correct to say that △PQD ~ △RPD? Why

Summary:

D is a point on side QR of △PQR such that PD⟂QR. △PQD is not similar to △RPD as it does not satisfy the property of similar triangles

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