1. Use Properties of Parallelograms
5.8
Use Properties of Parallelograms
Theorem 5.18
If a quadrilateral is a parallelogram, then its opposite sides are congruent. P S R Q
If PQRS is a parallelogram, then

2. Use Properties of Parallelograms
5.8
Use Properties of Parallelograms
Theorem 5.19
If a quadrilateral is a parallelogram, then its opposite angles are congruent. P S R Q
If PQRS is a parallelogram, then

3. Use Properties of Parallelograms
5.8
Use Properties of Parallelograms
Example 1
Use properties of parallelograms F J H G
Find the value of x and y.
Solution
FGHJ is a parallelogram by the definition of a parallelogram.
Use Theorem 5.18 to find the value of x.
Opposite sides of a are
Substitute x + 6 for FG and __ for ___.
Subtract 6 from both sides.
By Theorem 5.19,
In FGHJ, x = ___ and y = _____.

4. Use Properties of Parallelograms
5.8
Use Properties of Parallelograms
Theorem 5.20
If a quadrilateral is a parallelogram, then its consecutive angles are _______________.
supplementary P S R Q
If PQRS is a parallelogram, then

5. Use Properties of Parallelograms
5.8
Use Properties of Parallelograms
Example 2
Use properties of a parallelogram
Gates As shown, a gate contains several parallelograms. A D C B
Solution
By Theorem 5.20, the consecutive angle pairs in ABCD are ______________.
supplementary

6. Use Properties of Parallelograms
5.8
Use Properties of Parallelograms
Checkpoint. Find the indicated measure in LMN shown at the right. L K M N x
By Theorem 5.18, opposite sides are congruent.

7. Use Properties of Parallelograms
5.8
Use Properties of Parallelograms
Checkpoint. Find the indicated measure in LMN shown at the right. L K M N y
By Theorem 5.19, opposite angles are congruent.

8. Use Properties of Parallelograms
5.8
Use Properties of Parallelograms
Checkpoint. Find the indicated measure in LMN shown at the right. L K M N z
By Theorem 5.20, consecutive angles are supplementary.

9. Use Properties of Parallelograms
5.8
Use Properties of Parallelograms
Theorem 5.21
If a quadrilateral is a parallelogram, then its diagonals _________ each other.
bisect P S R Q

10. Use Properties of Parallelograms
5.8
Use Properties of Parallelograms
Example 3
Find the intersection of diagonals
The diagonals of STUV intersect at point W. Find the coordinates of W. T S W V U
Solution
By Theorem 5.21, the diagonals of a parallelogram _______ each other. So, W is the _________ of the diagonals TV and SU.
bisect
midpoint
Use the _____________________.
Midpoint Formula
Coordinates of the midpoint W of

11. Use Properties of Parallelograms
5.8
Use Properties of Parallelograms
Checkpoint. Complete the following exercises.
The diagonals of VWXY intersect at point Z. Find the coordinates of Z W V Z Y X
By Theorem 5.21, the diagonals of a parallelogram bisect each other. So, Z is the midpoint of the diagonals WY and VX.

12. Use Properties of Parallelograms
5.8
Use Properties of Parallelograms
Checkpoint. Complete the following exercises.
Given that FGHJ is a parallelogram, find MH and FH. F M J H G
By Theorem 5.21, the diagonals of a parallelogram bisect each other. So, M is the midpoint of the diagonal FH.

13. Use Properties of Parallelograms
5.8
Use Properties of Parallelograms
Pg. 318, 5.8 #2-34 even