Question

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

Answer 1

The correct option is B

similar but not congruent

Step 1: Use the given information.

Since two pairs of corresponding angles are equal, it implies that the third pair is also equal.

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

So, with the help of AAA similarity, it can be said that,

$∆\mathrm{ABC}~∆\mathrm{DEF}$

According to the provided information, the side $\mathrm{AB}$ is three times of side $\mathrm{DE}$ so, there is no similarity between the sides.

Therefore, the mentioned triangles are similar but not congruent.

Final answer:

Hence, the correct option is option B.