Transcript Section 6-3: Proving a Quadrilateral is a Parallelogram

Bellringer
Have your Homework (p. 356 #7-11, p. 364 #9-27
skip #13) and Notes out on your Desk
Work on p. 363 #1 – 5
SPI 3108.4.3 Identify, describe and/or
apply the relationships and theorems
involving different types of
quadrilaterals
Rules from Yesterday
If a quadrilateral is a parallelogram, then…
• Its opposite sides are parallel
• Its opposite sides are congruent
• Its consecutive angles are supplementary
• Its opposite angles are congruent
• Its diagonals bisect each other
Converses
If both pairs of opposite sides are parallel, …
If both pairs of opposite sides are congruent,…
If an angle is supplementary to both of its
consecutive angles,…
If both pairs of opposite angles are congruent, …
If the diagonals bisect each other, …
… Then the quadrilateral is a parallelogram!
One New Theorem…
If one pair of opposite sides is BOTH congruent
and parallel, then the quadrilateral is a
parallelogram
Questions
“Can you prove that the quadrilateral is a
parallelogram based on the given information?”
“For what values of x and y must ABCD be a
parallelogram?”
Classwork/Homework
6-3 Worksheet
Quiz on Friday