Question

All equilateral triangles are ________.
A) Congruent
B) Will be congruent if their length of sides are equal
C) Never congruent
D) none of these

Answer 1

Hint- Here we will use the property of equilateral triangles that equilateral triangles have all equal sides hence they are known as “regular triangles”. Using this property, we will solve this problem.
Complete step-by-step answer:
We need to select the correct option from the given below options:
For congruence of triangles, we need equal sides for two equilateral triangles, but here it has said nothing about sides of both triangles in option (A). So, this is incorrect. Here, it can be said that all equilateral triangles are similar.
Again, in option (B) it has been mentioned about the length of sides of the equilateral triangle. As it is given that if the length of sides is equal, then in that case it is congruent. As all angles are $60^\circ $ each and given all sides are equal then it can be said as congruent.
Hence, option (B) is correct.
Note- We should also remember the property of similarity of two triangles and congruence of two triangles. For similarity, it is not mandatory that sides should be equal or angles need to be equal. They should be in the same ratio. For congruence of triangles, sides and angles need to be equal.