Question

If the areas of two similar triangles are equal, then they are
A.Equilateral triangles
B.Isosceles triangles
C.Congruent triangles
D.Non-congruent triangles

Answer 1

Hint: We need to understand what exactly similar means and then we can select the correct option. Areas of two triangles are the same; it means two triangles have all sides the same and all angles are of the same measurements.

Complete step-by-step answer:
We will use elimination methods to solve the question.
Option D will be eliminated very first. Because the triangles that are not congruent cannot be similar. And the area will also not be equal.
Next we will see option A. In this option talking about the condition mentioned in the hint all equilateral triangles are having all angles of same measurement but not necessary that sides should be of same length. So it is eliminated.
Now option B isosceles triangle. All isosceles triangles need not have the same measurements. So it is eliminated.
Last is option C that is congruent. Yes it is the correct answer because congruent triangles have all sides the same and all angles are of the same measurement.
So option C is correct.

Note: Don’t get confused in similar and congruent because almost all students fail to distinguish it. Similar is related to only angles whereas congruence is all about sides and angles. Unless triangles are congruent areas cannot be the same.