1. EXAMPLE 1
Use a coordinate plane
Show that ORST is a trapezoid.
SOLUTION
Compare the slopes of opposite sides.
4 – 3
2 – 0 = 1 2
Slope of RS =
2 – 0
4 – 0 = 2 4 1
Slope of OT =
The slopes of RS and OT are the same, so RS OT .

2. EXAMPLE 1
Use a coordinate plane
2 – 4
4 – 2 = –2 2 –1
Slope of ST = 3
3 – 0
0 – 0 = ,
which is undefined
Slope of OR =
The slopes of ST and OR are not the same, so ST is not parallel to OR .
Because quadrilateral ORST has exactly one pair of parallel sides, it is a trapezoid.
ANSWER

3. GUIDED PRACTICE
for Example 1
1. What If? In Example 1, suppose the coordinates of point S are (4, 5). What type of quadrilateral is ORST? Explain.
SOLUTION
Compare the slopes of opposite sides.
5 – 3
4 – 0 = 1 2
Slope of RS =
2 – 0
4 – 0 = 1 2
Slope of OT =
The slopes of RS and OT are the same, so RS OT .

4. GUIDED PRACTICE
for Example 1
2 – 5
4 – 4 = –3
undefined
Slope of ST = 3
3 – 0
0 – 0 = ,
undefined
Slope of OR =
The slopes of ST and OR are the same, so ST is parallel to OR .
ANSWER
Parallelogram; opposite pairs of sides are parallel.

5. GUIDED PRACTICE
for Example 1
In Example 1, which of the interior angles of quadrilateral ORST are supplementary angles? Explain your reasoning. 2.
ANSWER
O and R , T and S are supplementary angles, as RS and OR are parallel lines cut by transversals OR and ST, therefore the pairs of consecutive interior angles are supplementary by theorem 8.5