Question

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

Answer 1

Converse of basic proportionality theorem:
If a line divides any two sides of a triangle in the same ratio then the line must be parallel to the third side.

GIVEN:
PS /SQ= PT/TR  & ∠PST = ∠PRQ.

We have,
PS /SQ= PT/TR

ST || QR
[By using the Converse of basic proportionality theorem]

∠PST  = ∠PQR     [corresponding angles]
∠PRQ  = ∠PQR    [ ∠PST = ∠PRQ]
PQ = PR

[Sides opposite to equal angles are equal]

Hence, ∆PQR is Isosceles .

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Answer 2

Step-by-step explanation:

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