∠ JEG≅∠ KFH
We can also look at the other pair of parallel segments.
Angles ∠ JGE and ∠ KHF are corresponding angles along the transversal GH, so these angles are also congruent.
∠ JGE≅∠ KHF
Let's focus now on the line with points E, F, G, and H.
It is given that segments EF and GH are congruent.
If we add segment FG to both of these, the Segment Addition Postulate guarantees that the resulting two segments are also congruent.
EG≅FH
Let's summarize what we know about triangles △ EJG and △ FKH.
We just proved that triangles △ EJG and △ FKH have two pairs of congruent angles and that the included sides are also congruent.
According to the Angle-Side-Angle (ASA) Congruence Postulate, the two triangles are congruent.
We can summarize the process above in a flow proof.
