Question

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

Answer 1

Let the two triangles be ABC and PQR. 

We have: 

∆ABC ~ ∆PQR, 

Here, 

BC = a, AC = b and AB = c 

PQ = r, PR = q and QR = p 

We have to prove:

a/p = b/q = c/r = a+b+c/p+q+r 

∆ABC ~ ∆PQR; therefore, their corresponding sides will be proportional.

This completes the proof.