Write a proof to show that opposite sides of a parallelogram are congruent. Be sure to create and name the appropriate geometric figures. This figure does not need to be submitted.
Given
Parallelogram .
What To Show
and
.
Proof
Draw diagonal .
Since is a transversal
to parallel lines
and
,
because they
are alternate interior angles.
Now, segment is congruent to itself (reflexive proeprty) so,
.
Since is
parallel to
,
because they
are alternate interior angles.
By ASA congruence, .
Since corresponding parts of congruent triangles are congruent,
and
.
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