Question

In∆ABC and ∆DEF if ∠ B = ∠ E, ∠ F = ∠ C and AB = 2DE, then two triangles are ?) *
1 point

1. congruent but not similar

2. similar but not congruent

3. neither congruent nor similar

4.congruent as well as similar​

Answer 1

Answer:

congruent but not similar

Answer 2

Concept:

Congruency and similarity.

Answer:

The correct answer is option 2. Similar but not congruent.

Given:

In ΔABC and ΔDEF,

∠B=∠E,∠F=∠C

AB = 2DE

Find:

Check whether the triangles are similar or congruent.

Solution:

In ΔABC and ΔDEF,

∠B=∠E,   ∠F=∠C

Then, by angle sum property the third angles of both the triangles are also equal i.e., ∠A=∠D

Hence, by the AAA criterion, the triangles ΔABC and ΔDEF are similar.

AB = 2DE

It is clear that AB and DE are not equal to each other.

Hence, the triangles are not congruent because for congruency the sides of triangles should be equal.

Therefore, option 2 is correct i.e., ΔABC and ΔDEF are similar but not congruent.

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