# Prove that the ra

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)

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