CBSE Class 10 Maths Question Paper 2018 | Q17B

Question 17B: If the area of two similar triangles are equal, prove that they are congruent.

Video Explanation

Explanatory Answer | CBSE 2018 3 Mark Question 17B

Theorem: Ratio of the areas of two similar triangles is the square of the ratio of their corresponding sides.

Triangle 1 and triangle 2 are similar.

Let their corresponding sides be in the ratio x : y
∴ The ratio of their areas is x² : y²
If their areas are equal, x² = y².
Then, x = y

So, the corresponding sides of the 2 similar triangles are equal.
2 similar triangles whose corresponding sides are equal are congruent triangles.