Question

In the given figure, Sand Tare points on sides PQ and PR, respectively of ΔPQR such that ST is parallel to QR and SQ = TR. Prove that ΔPQR is an isosceles triangles.

Answer 1

Given: In ΔPQR, ST || QR and SQ = TR.

To prove: ΔPQR is an isosceles triangle.

Proof: ST || QR.

As a result of the basic proportionality theorem,

`(PS)/(SQ) = (PT)/(TR)`  ......(i)

Now, SQ = TR  ......(ii)

∴ `(PS)/(TR) = (PT)/(TR)`

⇒ PS = PT  ......(iii)

Adding equations (ii) and (iii),

PS + SQ = PT + TR

⇒ PQ = PR

Since, PQ = PR

Thus, ΔPQR is an isosceles triangle.

Hence proved.