CBSE Class 10 Maths Question Paper 2018 | Q17B

CBSE Solved Question Paper 3 Mark | Similar & Congruent Triangles

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

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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.


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