Question

In $△ABC$ and $△DEF,\angle B\cong \angle F,\angle F=\angle C$ and $AB=3DE$ then which of the statements regarding to two triangle is ture?

• A. The triangles are not congruent and not similar
• B. The triangles are similar but not congruent
• C. The triangles are congruent and similar.
• D. None of the statement above is true.

Answer 1

The correct option is B The triangles are similar but not congruent

Given: $\angle B=\angle E,\angle F=\angle C$ and $AB=3DE\Rightarrow \frac{AB}{DE}=\frac{3}{1}$

Proof: In $△ABC$ and $△DEF$

$\angle B=\angle E$

$\angle C=\angle F$

$\therefore △ABC\sim △DEF$[By $AA$ criteria]

Since there is no any congruency criteria like $AA$.

Thus, $△ABC$ and $△DEF$ are not congruent.

Hence, the given triangles are similar but not congruent.

So, $\text{B}$ is the correct option.