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

Question

Philoid · Accepted Answer

Let ∆ ABC and ∆ DEF be two similar triangles, i.e., ∆ ABC ∼ ∆ DEF.

⇒ Ratio of all the corresponding sides of ∆ ABC and ∆ DEF are equal.

Let these ratios be equal to some number α.

⇒ AB = α DE, BC = α EF, AC = α DF ……….(i)

Now, perimeter of ∆ ABC = AB + BC + AC

= α DE + α EF + α DF [ From (i)]

= α (DE + EF + DF)

= α (perimeter of ∆ DEF)