You have to show that corresponding sides and corresponding angles are congruent.
See solution.
Practice makes perfect
To prove that these triangles are congruent, △ ABG ≅ △ DCF, we have to show that corresponding sides are congruent and that corresponding angles are congruent. Let's separate the two triangles a bit.
Sides
We already know that two of the triangles sides, are congruent: AB≅ CD and AG≅ DF. To prove that the remaining sides are congruent as well, we can use the following fact.
BE≅ EG≅ FE≅ EC
BG is cut in two congruent pieces and so is FC. What the statement above tells us is that all of these four smaller pieces are congruent. Thus, we can create an equation using their measures.
BE+ EG=FE+ EC
In other words, BG≅ CF
Angles
As with the sides, we know that two of the angles are congruent. According to the Third Angles Theorem, if two angles of one triangle are congruent to two angles of another triangle, then the third angles are also congruent.
Since corresponding sides and corresponding angles are congruent, we have proven that △ ABG ≅ △ DCF.
