Definition:
A parallelogram is a quadrilateral with both pairs of
opposite sides parallel. 
*Parallelogram
I
have:
 2 sets of parallel sides
 2 sets of congruent sides
 opposite angles congruent
 consecutive angles supplementary
 diagonals bisect each other
 diagonals form 2 congruent triangles 

Using this definition, the remaining properties
regarding a parallelogram can be "proven" true and become theorems.
When GIVEN a
parallelogram, the definition and theorems are stated as ... 
When trying to
PROVE a
parallelogram, the definition and theorems are stated as ...
(many of these theorems
are converses of the previous theorems) 
Proof of Theorem: If a quadrilateral is a
parallelogram, the 2 pairs of opposite sides are
congruent.
(Remember: when attempting to prove a theorem to be
true,
you cannot use the theorem as a reason in your proof.)
STATEMENTS 
REASONS 
1 

1 
Given 
2 
Draw segment from
A to C 
2 
Two points determine
exactly one line. 
3 

3 
A parallelogram
is a quadrilateral with both pairs of opposite sides parallel. 
4 

4 
If two
parallel lines are cut by a transversal, the alternate interior
angles are congruent. 
5 

5 
Reflexive property:
A quantity is congruent to itself. 
6 

6 
ASA: If two
angles and the included side of one triangle are congruent to
the corresponding parts of another triangle, the triangles are
congruent. 
7 

7 
CPCTC:
Corresponding parts of congruent triangles are congruent. 
Proof of Theorem: If
ONE PAIR of opposite sides of a
quadrilateral are BOTH parallel and congruent, the quadrilateral is
a parallelogram.
(Remember: when attempting to prove a theorem to be true,
you cannot use the theorem as a reason in your proof.)
STATEMENTS 
REASONS 
1 

1 
Given 
2 
Draw segment from
A to C 
2 
Two points determine
exactly one line. 
3 

3 
If two parallel
lines are cut by a transversal, the alternate interior angles
are congruent. 
4 

4 
Reflexive property: A quantity is congruent to itself. 
5 

5 
SAS: If two
sides and the included angle of one triangle are congruent to
the corresponding parts of another triangle, the triangles are
congruent. 
6 

6 
CPCTC:
Corresponding parts of congruent triangles are congruent. 
7 

7 
If two lines are cut
by a transversal and the alternate interior angles are
congruent, the lines are parallel. 
8 

8 
A parallelogram
is a quadrilateral with both pairs of opposite sides parallel. 
