Answer
a. Definition of a parallelogram
b. Alternate interior angles are congruent.
c. Opposite sides of a parallelogram are congruent.
d. $\triangle ABE$ is congruent to $\triangle CDE$.
e. Corresponding parts of congruent triangles are congruent.
f. $\overline{AC}$ and $\overline{BD}$ bisect each other at point $E$.
Work Step by Step
a. Opposite sides are parallel in a parallelogram, which is the definition of a parallelogram.
b. Alternate interior angles are congruent when two parallel lines are cut by a transversal.
c. Opposite sides of a parallelogram are congruent.
d. $\triangle ABE$ is congruent to $\triangle CDE$.
e. Corresponding parts of congruent triangles are congruent.
f. $\overline{AC}$ and $\overline{BD}$ bisect each other at point $E$.
