1. 6.2-6.3: Parallelograms Objectives:
Be able to use some properties of parallelograms.
Be able to prove that a quadrilateral is a parallelogram.

2. Parallelograms
A parallelogram is a quadrilateral with both pairs of opposite sides parallel.
REMEMBER,
If two lines are parallel, then: P S
1) Alternate interior angles are congruent
2) Alternate exterior angles are congruent
3) Corresponding angles are congruent
4) Same-side interior angles are supplementary. Q R
When you mark diagrams of quadrilaterals, use matching arrowheads to indicate which sides are parallel. For example, in the diagram above, PQ║RS and QR║SP. The symbol PQRS is read “parallelogram PQRS.”

3. Theorems about Parallelograms
Thm 6.2
If a quadrilateral is a parallelogram, then its opposite sides are congruent.
Thm 6.3
If a quadrilateral is a parallelogram, then the opposite angles are congruent.
Thm 6.4
If a quadrilateral is a parallelogram, then its consecutive angles are supplementary.
Thm 6.5
If a quadrilateral is a parallelogram, then its diagonals bisect each other. S P Q R P S R Q P S R Q P S M R Q

4. Example
1) Find the value of each variable in the parallelogram below.

5. Example: W Z Y X

6. Example: P S P Q Q R

7. Example:

8. Theorems about Parallelograms
Thm 6.6
If both pairs of opposite sides are congruent, then the quadrilateral is a parallelogram.
Thm 6.7
If both pairs of opposite angles are congruent, then the quadrilateral is a parallelogram.
Thm 6.8
If an angle of a quadrilateral is supplementary to both of its consecutive angles, then the quadrilateral is a parallelogram.
Thm 6.9
If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram. S P Q R P S R Q P S R Q P S R Q

9. Proving Quadrilateral are Parallelograms
Theorems about Parallelograms
Thm 6.10
If one pair of opposite sides of a quadrilateral are congruent and parallel, then the quadrilateral is a parallelogram S P Q R
Summary
Proving Quadrilateral are Parallelograms
Show that both pairs of opposite sides are parallel
Show that both pairs of opposite sides are congruent
Show that both pairs of opposite angles are congruent
Show that one angle is supplementary to both consecutive angles
Show that the diagonals bisect each other
Show that one pair of opposite sides are congruent and parallel

10. Assignment: Read pages 330-333 and 338-341 Pages 333-334 #4-36 EVENS
Pages #9-19 ALL