Section 5-2
Proving a Quadrilateral is a
Parallelogram
There are 5 ways to prove that a quadrilateral is a
parallelogram. They are…
1. If both pairs of opposite sides of a quadrilateral are
parallel, then it is a parallelogram. (Definition of a
Parallelogram).
2. If both pairs of opposite sides of a quadrilateral are
congruent, then it is a parallelogram.
3. If one pair of opposite sides of a quadrilateral are both
congruent and parallel, then it is a parallelogram.
4. If both pairs of opposite angles of a quadrilateral are
congruent, then it is a parallelogram.
5. If the diagonals of a quadrilateral bisect one another,
then it is a parallelogram.
You will be asked to list
these 5 ways of proving
a quadrilateral is a
parallelogram on your
next test.
Check for Understanding – Examine the markings on
each quadrilateral. Determine whether there is
enough information to prove that the quadrilateral is
a parallelogram. If there is, write the justification.
9
12
8
8
12
Yes. If both pairs of
opposite sides in a
quadrilateral are
congruent, then it is a
parallelogram.
9
Yes. If one pair of
opposite sides of a
quadrilateral are both
congruent and parallel, then
it is a parallelogram.
Check for Understanding – Examine the markings on
each quadrilateral. Determine whether there is
enough information to prove that the quadrilateral is
a parallelogram. If there is, write the justification.
70
70
Yes. If the diagonals of
a quadrilateral bisect
one another, then it is a
parallelogram.
No! We need BOTH pairs
of opposite angles to be
congruent.
Check for Understanding – Examine the markings on
each quadrilateral. Determine whether there is
enough information to prove that the quadrilateral is
a parallelogram. If there is, write the justification.
70
110
70
Yes. If both pairs of
opposite angles of a
quadrilateral are congruent,
then it is a parallelogram.
Yes. Definition of a
parallelogram.
Check for Understanding – Examine the markings on
each quadrilateral. Determine whether there is
enough information to prove that the quadrilateral is
a parallelogram. If there is, write the justification.
No!
No! To use the reason
“If one pair of sides of
a quadrilateral is both
parallel and congruent,
it has to be the SAME
PAIR!