Question

In triangle PQR, PQ=PR. Prove that angle R=angle Q

Answer 1

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Answer 2

Explanation:

Given that PQR is a triangle.

Also, PQ = PR

To prove: $\angle R=\angle Q$

Let us draw PT perpendicular to QR

Thus, PT is a bisector of ∠QPR

Let us consider the triangles QPT and RPT

PQ = PR (Given)

The line PT is common to both the triangles.

PT = PT (Common side)

Then,

∠QPT = ∠RPT

Then, by SAS property, we have,

ΔQPT ≅ ΔRPT

Applying the CPCT theorem, we get,

$\angle R=\angle Q$

Hence proved.

Learn more:

(1) In fig PQ= PR and angle q= angle R prove that triangle pqs = triangle prt, qs=rt

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(2) PQ = PR and ∠Q = ∠R. Prove that ΔPQS≅ ΔPRT.

brainly.in/question/5967205