SOLUTION: In triangle ABC, the measure of angle A=36 AB=22, and AC=12; in triangle DEF the measure of angle D=36, DE=44, and DF=24. Justify whether or not the triangles are similar.

Algebra ->  Triangles -> SOLUTION: In triangle ABC, the measure of angle A=36 AB=22, and AC=12; in triangle DEF the measure of angle D=36, DE=44, and DF=24. Justify whether or not the triangles are similar.      Log On


   

Question 397236: In triangle ABC, the measure of angle A=36 AB=22, and AC=12; in triangle DEF the measure of angle D=36, DE=44, and DF=24. Justify whether or not the triangles are similar.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
Triangles are similar if they have the same shape, but can be different sizes.
In your case triangle ABC, the measure of angle A=36,+AB=22,
and AC=12;
and in triangle DEF the measure of angle D=36, DE=44, and
DF=24.
as we can see:
1. corresponding+angles are the same; A=D=36
2. Corresponding+sides are all in the same+proportion
Above, DE is twice the length of AB.
Therefore, the other pairs of sides are also in that proportion. DF is
twice AC and BC is twice+EF.
Formally, in two+similar triangles ABC and DEF you have:
DE%2FAB=DF%2FAC=BC%2FEF

so, your triangles are similar