# 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

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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.

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