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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.
Solution
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.
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