Perimeter of Similar Triangle Theorem

Theorem : Prove that the ratio of the perimeters of two similar triangles is the same as the ratio of their corresponding sides.

Given : Two ΔABC and ΔPQR such that ΔABC~ΔPQR.

To Prove :

Proof :

ΔABC~ΔPQR (Given)

[corresponding sides parts of similar triangle are proportional]

Let

Adding equation (2), (3) and (4)

AB + BC + CA = k.PQ + k.QR + k.RP
AB + BC + CA = k (PQ + QR + RP)

Using equation (1) and (5)

Hence Proved

Class 10