Question

In the given figure, PS/SQ = PT/TR and ∠ PST = ∠ PRQ. Prove that PQR is an isosceles triangle.


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Answer 1

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Answer 2

Answer:

ANSWER

We have,

SQ

PS

=

TR

PT

⇒ ST∣∣QR [By using the converse of Basic Proportionality Theorem]

⇒ ∠PST=∠PQR [Corresponding angles]

⇒ ∠PRQ=∠PQR [∵∠PST=∠PRQ (Given)]

⇒ PQ=PR [∵ Sides opposite to equal angles are equal]

⇒ △PQR is isoscele