This document contains notes from a geometry lesson on five ways to prove that a quadrilateral is a parallelogram. It lists the five properties: 1) both pairs of opposite sides are parallel, 2) both pairs of opposite sides are congruent, 3) one pair of opposite sides are parallel and congruent, 4) the diagonals bisect each other, and 5) both pairs of opposite angles are congruent. It directs students to examples in the textbook and ends with an exit slip quiz and assigning homework problems.

1. Geom5­6.notebook December 01, 2011
BELL WORK: Please copy the picture and info for #15 on
p.246. Get started, and do as much as you can.
Thank you! D C
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Questions on p.244 #1­7,11,12?
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2. Geom5­6.notebook December 01, 2011
Aftertoday'slesson,youwillknow5waystoprove
thataquadrilateralisaparallelogram!
5.6 on p.249:
You can prove that a quadrilateral is a parallelogram in many ways!
1. If both pairs of opposite sides of a quadrilateral are parallel,
then the quadrilateral is a parallelogram (reverse of def.).
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3. Geom5­6.notebook December 01, 2011
2. If both pairs of opposite sides of a quadrilateral are congruent,
then the quadrilateral is a parallelogram (converse of prop.).
3. If one pair of opposite sides of a quadrilateral are both parallel and
congruent, then the quadrilateral is a parallelogram.
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4. Geom5­6.notebook December 01, 2011
4. If the diagonals of a quadrilateral bisect each other,
then the quadrilateral is a parallelogram (converse of prop.).
5. If both pair of opposite angles of a quadrilateral are congruent,
then the quadrilateral is a parallelogram (converse of prop.).
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5. Geom5­6.notebook December 01, 2011
These are outlined on p.249 if you ever need a reference!
Also, this section has 3 examples of proofs that use these.
Take a look! The book is your friend.
EXIT SLIP: Answer Always, Sometimes, or Never.
A quadrilateral is a parallelogram if
a) diagonals are congruent.
b) one pair of opposite sides are congruent and one pair of
opposite sides are parallel.
c) each pair of consecutive angles are supplementary.
d) all angles are right angles.
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6. Geom5­6.notebook December 01, 2011
5.4­5.6 Quiz on Friday
homework: p. 251 #1­5,7,8
due Friday
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