Question

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

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Answer 1

Answer:

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Answer 2

Answer:

Given:

\dfrac{PS}{SQ}=\dfrac{PT}{TR}

SQ

PS

=

TR

PT

To Prove That:

PQR is an isosceles triangle.

Proof:

According to Basic Proportionality Theorem:

A line divides any two sides of a triangle in the same ratio, then the line is parallel to the third side.

Therefore by this:

ST ║QR

∠ PST = ∠ PQR (Corresponding angles) ……..Equation (i)

∠ PST = ∠ PRQ (Given)------Equation (ii)

From equation (i) and equation (ii),

∠ PRQ = ∠ PQR

From this we can say that:

PQ = PR (Sides opposite the equal angles are equal)

Therefore we can say that PQR is an isosceles triangle.