Question

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

Answer 1

Let there are two traingles ABC and PQR such that ABC~PQR.
=>AB = BC = AC
PQ QR PR
Let AB = BC = AC = k
PQ QR PR
=> AB= PQ * k ...................(i)
BC= QR * k .....................(ii)
AC= PR * k ....................(iii)
Add (i), (ii) and (iii)
=> AB+BC+AC= k * (PQ+QR+PR)
=> (AB+BC+AC) = k
(PQ+QR+PR)
But k =AB = BC = AC
PQ QR PR
Hence (AB+BC+AC) = AB = BC = AC
(PQ+QR+PR) PQ QR PR