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Geometry
Notes – Lesson 6.3
Name _______________________________________
What Do We Already Know?
If a quadrilateral is a parallelogram then . . .
 both pairs of opposite sides are ________________________.

both pairs of opposite sides __________________________.

both pairs of opposite angles are __________________________.

diagonals of the parallelogram ________________ each other.

consecutive angles are ________________________________.
To prove a quadrilateral is a parallelogram, one of the following must be given:
Theorem 6.5: If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
Proof:

Teorem 6.6: If both pairs of opposite angles of a quadrilateral are congruent,
then the quadrilateral is a parallelogram.

Theorem 6.7: If the diagonals of a quadrilateral bisect each other, then the
quadrilateral is a parallelogram.

Theorem 6.8: If one pair of opposite sides of a quadrilateral is both congruent
and parallel, then the quadrilateral is a parallelogram.
Examples. Can you prove the quadrilateral is a parallelogram from what is given?
Find the values of the missing variables for which the figure must be a parallelogram.
Find the value of x. Then tell whether the figure must be a parallelogram. Explain your answer.