Choose the correct answer from the given four options:
In triangles $ \mathrm{ABC} $ and $ \mathrm{DEF}, \angle \mathrm{B}=\angle \mathrm{E}, \angle \mathrm{F}=\angle \mathrm{C} $ and $ \mathrm{AB}=3 \mathrm{DE} $. Then, the two triangles are
(A) congruent but not similar
(B) similar but not congruent
(C) neither congruent nor similar
(D) congruent as well as similar

AcademicMathematicsNCERTClass 10

Given:

In triangles \( \mathrm{ABC} \) and \( \mathrm{DEF}, \angle \mathrm{B}=\angle \mathrm{E}, \angle \mathrm{F}=\angle \mathrm{C} \) and \( \mathrm{AB}=3 \mathrm{DE} \). 

To do:

We have to choose the correct answer.

Solution:


In triangles \( \mathrm{ABC} \) and \( \mathrm{DEF}, \angle \mathrm{B}=\angle \mathrm{E}, \angle \mathrm{F}=\angle \mathrm{C} \) and \( \mathrm{AB}=3 \mathrm{DE} \). 

This implies,

$\angle \mathrm{A}=\angle \mathrm{D}$

We know that,

If in two triangles corresponding two angles are same, then they are similar by AAA similarity criterion.

Here,

$\triangle ABC$ and $\triangle DEF$ do not satisfy any rule of congruency, (SAS, ASA, SSS).

Therefore, triangles \( \mathrm{ABC} \) and \( \mathrm{DEF} \) are similar but not congruent.

raja
Updated on 10-Oct-2022 13:27:52

Advertisements