1. EXAMPLE 4
Use coordinate geometry
Show that quadrilateral ABCD is a parallelogram.
SOLUTION
One way is to show that a pair of sides are congruent and parallel. Then apply Theorem 8.9.
First use the Distance Formula to show that AB and CD are congruent.
AB = =
[2 – (–3)]2 + (5 – 3)2 29
CD =
(5 – 0)2 + (2 – 0)2 = 29

2. EXAMPLE 4
Use coordinate geometry
Because AB = CD =
29 , AB
CD.
Then use the slope formula to show that AB
CD.
5 – (3)
2 – (–3) = 2 5
2 – 0
5 – 0 = 2 5
Slope of AB =
Slope of CD =
Because AB and CD have the same slope, they are parallel.
AB and CD are congruent and parallel. So, ABCD is a parallelogram by Theorem 8.9.
ANSWER

3. EXAMPLE 4
GUIDED PRACTICE
for Example 4
6. Refer to the Concept Summary. Explain how other methods can be used to show that quadrilateral ABCD in Example 4 is a parallelogram.
Find the slopes of all four sides and show that opposite are parallel.
A second way is to find the lengths of each side and show that opposite sides are congruent.
A third way is to find the point of intersection of the diagonals and show the diagonals bisect each other.
ANSWER