1. 6.3 Proving that a Quadrilateral is a Parallelogram
If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

2. Theorem 6.9
If an angle of a quadrilateral is supplementary to both of its consecutive angles, then the quadrilateral is a parallelogram.

3. Theorem 6.10
If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

4. Finding Values for Parallelograms
For what value of y must PQRS be a parallelogram?
3x – 5 = 2x + 1
x – 5 = 1
x = 6
y = x + 2
y = 6 + 2
y = 8

5. Theorem 6.11
If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.

6. Theorem 6.12
If one pair of opposite sides of a quadrilateral is both congruent and parallel, then the quadrilateral is a parallelogram.

7. Deciding Whether a Quadrilateral is a Parallelogram
Can you prove that the quadrilateral is a parallelogram based on the diagram? Explain.
No. You need to show that both pairs of opposite sides are congruent, not consecutive sides.
Yes, same-side interior angles are supplementary, making segment AB and segment DC parallel. Since segment AB is congruent to segment DC, ABCD is a parallelogram.

8. Concept Summary Proving that a Quadrilateral is a Parallelogram

9. More Practice!!!!!
Homework – Textbook p. 372 #7 – 16 ALL.