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Prove that the ratio of the perimeters of two similar triangles is the same as the ratio of their corresponding sides.
Prove that the ratio of the perimeters of two similar triangles is the same as the ratio of their corresponding sides.
CBSE | Class 10 | maths | Maths | ML Aggarwal | Similarity
Prove that the ratio of the perimeters of two similar triangles is the same as the ratio of their corresponding sides.

Solution:-

Consider the two triangles, ∆MNO and ∆XYZ

From the question it is given that, two triangles are similar triangles

So, ∆MNO ~ ∆XYZ

If two triangles are similar, the corresponding angles are equal and their corresponding sides are proportional.

MN/XY = NO/YZ = MO/XZ

Perimeter of ∆MNO = MN + NO + MO

Perimeter of ∆XYZ = XY + YZ + XZ

Therefore, (MN/XY = NO/YZ = MO/XZ) = (MN/XY + NO/YZ + MO/XZ)

= Perimeter of ∆MNO/perimeter of ∆XYZ

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