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

Asked by  | 19th Jul, 2013, 10:00: AM

Expert Answer:

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.

Answered by  | 21st Jul, 2013, 01:22: PM

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