Question

han has proven that △abc is congruent to △dcb using the side - side - side triangle congruence theorem. why can he now conclude that $overline{ab}paralleloverline{cd}$?

Explanation:

Since $\triangle ABC\cong\triangle DCB$ by SSS, corresponding angles are equal. $\angle ABC$ and $\angle DCB$ are alternate - interior angles. If alternate - interior angles are equal, then the lines are parallel.

Answer:

Because corresponding angles from congruent triangles (alternate - interior angles $\angle ABC$ and $\angle DCB$) are equal, and if alternate - interior angles are equal, then $\overline{AB}\parallel\overline{CD}$.