On this page, we hope to clear up problems that you might have
with parallelograms. A parallelogram is a special kind of
quadrilateral. There are many special rules and theorems that
apply to parallelograms only. By scrolling down or clicking
on the link below, you will be on your way to understanding
Quiz on Parallelograms
A parallelogram is so named because it has two pairs
of opposite sides that are
Problem: Prove triangle ABC is congruent to triangle CDA. Solution: Since the figure is a parallelogram, segment AB is parallel to segment DC and the two segments are also congruent. Angle 2 is congruent to angle 4 and angle 1 is congruent to angle 3. This is true because alternate interior angles are congruent when parallel lines are cut by a transversal. Segment AC is congruent to segment CA by the Reflexive Property of Congruence, which says any figure is congruent to itself. Triangle ABC is congruent triangle CDA by Angle-Side-Angle
2. Both pairs of opposite sides of a parallelogram
Problem: Prove segment AE is congruent to segment CE and segment DE is congruent to segment BE. Solution: By the definition of a parallelogram, segment AD and segment BC are parallel and congruent. Angle 1 is congruent to angle 3 and angle 2 is congruent to angle 4. This is true because alternate interior angles are congruent when parallel lines are cut by a transversal. Triangle AED and triangle CEB are congruent by Angle-Side-Angle. The segments we were asked to prove as congruent are congruent by CPCTC.
In this section, we hope to clear up problems associated with
figuring out if a given quadrilateral is a parallelogram. Most
of the theorems that help us figure out if a shape is a parallelogram
are the converses of the theorems stated above.
Take the Quiz on parallelograms. (Very useful to review or to see if you've really got this topic down.) Do it!