A parallelogram is a quadrilateral whose opposite sides are parallel. In the figure below, is a parallelogram. is parallel to and is parallel to .
In this post, aside from being parallel, we will also prove that the opposite sides of a parallelogram are congruent.
The opposite sides of a parallelogram are congruent.
What To Show
Draw diagonal .
Since is a transversal to parallel lines and , because they are alternate interior angles. (A)
Now, segment is congruent to itself (reflexive proeprty) so, . (S)
Since is parallel to , because they are alternate interior angles. (A)
By ASA congruence, .
Since corresponding parts of congruent triangles are congruent, and .