Choose the correct answer from the given four options:
If in two triangles $ \mathrm{DEF} $ and $ \mathrm{PQR}, \angle \mathrm{D}=\angle \mathrm{Q} $ and $ \angle \mathrm{R}=\angle \mathrm{E} $, then which of the following is not true?
(A) $ \frac{\mathrm{EF}}{\mathrm{PR}}=\frac{\mathrm{DF}}{\mathrm{PQ}} $
(B) $ \frac{\mathrm{DE}}{\mathrm{PQ}}=\frac{\mathrm{EF}}{\mathrm{RP}} $
(C) $ \frac{\mathrm{DE}}{\mathrm{QR}}=\frac{\mathrm{DF}}{\mathrm{PQ}} $
(D) $ \frac{E F}{R P}=\frac{D E}{Q R} $

Given:

In two triangles \( \mathrm{DEF} \) and \( \mathrm{PQR}, \angle \mathrm{D}=\angle \mathrm{Q} \) and \( \angle \mathrm{R}=\angle \mathrm{E} \).

To do:

We have to find the statement that is not true.

Solution:

In $\triangle D E F$ and $\triangle PQR$,

$\angle D=\angle Q$

$\angle R=\angle E$

Therefore, by AAA similarity,

$\triangle D E F \sim \triangle Q R P$

This implies,

$\angle F=\angle P$         (Corresponding angles of similar triangles)

Therefore,

$\frac{D F}{Q P}=\frac{E D}{R Q}=\frac{F E}{P R}$ 

Hence, (B) \( \frac{\mathrm{DE}}{\mathrm{PQ}}=\frac{\mathrm{EF}}{\mathrm{RP}} \) is not true.

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Updated on: 10-Oct-2022

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