CPM Homework Help : GC Problem 5-79

Lizzie noticed that two angles in $ΔDEF$ , shown below, have the same measure. Based on this information, what statement can you make about the relationship between $\overline{DE}$ and $\overline{EF}$ ?
Triangle D, E, F, has two angles 54 degrees and 54 degrees between side D, F.

Answer:

They must have equal lengths, because if base angles are equal, then the sides opposite them are equal and the triangle is isosceles.