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

We know that if two triangles are similar then the ratio of their corresponding sides are equal.

Hence, if triangle ABC is similar to triangle PQR, we have:

AB/ PQ = BC/ QR = AC/ PR

 

Now, using a property of ratios, we have:

AB/ PQ = BC/ QR = AC/ PR = AB+BC+CA/ PQ+QR+PR

 

Hence, the ratio of the perimeters of two similar triangles is the same as the ratio of their corresponding sides.