Choose the correct answer from the given four options: In triangl… - Vidyadip

MCQ

Choose the correct answer from the given four options:
In triangles ABC and DEF, $\angle\text{B}=\angle\text{E},\angle\text{F}=\angle\text{C}\ \text{and}\text{ AB}=3\text{ DE}.$ Then, the two triangles are:

A
Congruent but not similar.
✓
Similar but not congruent.
C
Neither congruent nor similar.
D
Congruent as well as similar.

✓

Answer

Correct option: B.

Similar but not congruent.

$\text{In}\ \triangle\text{ABC}\text{ and}\ \triangle\text{DEF}, \angle\text{B}=\angle\text{E}=\angle\text{F}\ \text{and}=\text{AB}=3\text{DE}$

We know that, if in two triangles corresponding two angles are same, then they are similar by AAA similarity criterion. Also $\triangle\text{ABC}\text{ and}\ \triangle\text{DEF}$ do not satisfy any rule of congruency, (SAS, ASA, SSS), so both are not congruent.

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