Choose the correct answer from the given four options:
If in two triangles $ \mathrm{ABC} $ and $ \mathrm{PQR}, \frac{\mathrm{AB}}{\mathrm{QR}}=\frac{\mathrm{BC}}{\mathrm{PR}}=\frac{\mathrm{CA}}{\mathrm{PQ}} $, then
(A) $ \triangle \mathrm{PQR} \sim \triangle \mathrm{CAB} $
(B) $ \triangle \mathrm{PQR} \sim \triangle \mathrm{ABC} $
(C) $ \triangle \mathrm{CBA} \sim \triangle \mathrm{PQR} $
(D) $ \triangle \mathrm{BCA} \sim \triangle \mathrm{PQR} $

Given:

In two triangles \( \mathrm{ABC} \) and \( \mathrm{PQR}, \frac{\mathrm{AB}}{\mathrm{QR}}=\frac{\mathrm{BC}}{\mathrm{PR}}=\frac{\mathrm{CA}}{\mathrm{PQ}} \)

To do:

We have to choose the correct answer.

Solution:

In $\triangle A B C$ and $\triangle P Q R$,

$\frac{\mathrm{AB}}{\mathrm{QR}}=\frac{\mathrm{BC}}{\mathrm{PR}}=\frac{\mathrm{CA}}{\mathrm{PQ}}$

We know that,

If the sides of one triangle are proportional to the side of the other triangle and their corresponding angles are also equal, then both the triangles are similar by SSS similarity.

Therefore,

$\triangle \mathrm{PQR} \sim \triangle \mathrm{CAB}$

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Simply Easy Learning

Updated on: 10-Oct-2022

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