Question

in the figure, segment AB is parallel to CD, XY is the perpendicularbisector of AB, E is the midpoint of XY. Prove that AAEB SADEC.

Answer 1

Given that segment AB is prallel to segment CD, we can treat segment AD as their transversal.

$\angle BAE=\angle CDE$

Since they are alternate angles.

Next, since segments AD and BC intersects at E,

$\angle AEB=\angle DEC$

Since the two angles are an example of opposite angles, and opposite angles have equal measurement.