The distance around a triangle is 38 centimeters. If two sides are equal and the length of the third side is 12 centimeters, what is the length of each of the other two sides?

the answer is 13

Step-by-step explanation:

You subtract 12 from 38 which is 26 then divide that by 2

If we're trying to prove similarity, it's only sufficient to prove two angles are equal, because by def, the third angle must be equal.

in  δabc and  δgef,
∠abc =  ∠dec (given)
but,  ∠dec =  ∠feg (vertically opposite angles)
∴  ∠abc =  ∠feg

similarly,  ∠gfe =  ∠dce (given)
but,  ∠dce =  ∠bca (vertically opposite angles are equal)
∴  ∠gfe =  ∠bca

since two angles are equal, by definition, the third angle must be equal, and hence, we've proved the two triangles are similar as they are equi-angular.