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
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.
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