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

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

Using equation (1) and (5)
Hence Proved