Theorem 5.18

1
Theorem 5.18
If a quadrilateral is a parallelogram, then its
opposite sides are congruent.
If PQRS is a parallelogram, then
2
Theorem 5.19
If a quadrilateral is a parallelogram, then its
opposite angles are congruent.
If PQRS is a parallelogram, then
3
Use properties of parallelograms
Example 1
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.
Substitute x 6 for FG and __ for ___.
Subtract 6 from both sides.
4
Theorem 5.20
If a quadrilateral is a parallelogram, then its
consecutive angles are _______________.
supplementary
If PQRS is a parallelogram, then
5
Use properties of a parallelogram
Example 2
Gates As shown, a gate contains several
parallelograms.
Solution
supplementary
6

1. x

By Theorem 5.18, opposite sides are congruent.
7

1. y

By Theorem 5.19, opposite angles are congruent.
8

1. z

By Theorem 5.20, consecutive angles are
supplementary.
9
Theorem 5.21
If a quadrilateral is a parallelogram, then its
diagonals _________ each other.
bisect
10
Find the intersection of diagonals
Example 3
Solution
bisect
midpoint
Midpoint Formula
Use the _____________________.
Coordinates of the midpoint W of
11
Checkpoint. Complete the following exercises.
12
Checkpoint. Complete the following exercises.
13
Pg. 318, 5.8 2-34 even