Question

Two similar triangles always have the same area. Explain with reasons, whether the given statement are true or false.

Answer 1

Hey there!

We know that,

Ratio of corresponding areas of two similar triangles are equal to square of the ratio of any corresponding sides.

So, If the sides are equal. The areas would be equal.

But if we have the sides equal, then the triangles be called Congruent triangles.

So, Two similar triangles need not have same areas.

We can say that, Ratio of areas of similar triangles is equal to ratio of square of corresponding sides.

Therefore, The above statement " Two similar triangles always have the same area. " is false.

Hope helped!