In the diagram, m∠f = 60°.

to prove that the triangles are similar by the sas similarity theorem, it needs to be proven that .
a) angle j measures 60
b) angle j measures 30
c) angle i measures 60
d) angle i measures 30

1. The Side Angle Side (SAS) similarity theorem states that:

If two sides of a triangle are proportional to 2 sides of another triangle, and the angles around each of these 2 pairs f sides are equal (congruent), then the triangles are similar.

2. That is, we notice the equivalent ratios:

 

so

then if m(I)=m(F)=60°, the triangles EFG and HIJ are similar, by SAS similarity theorem.