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EXAMPLE 1

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

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EXAMPLE 1

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  1. Show that ORSTis a trapezoid. = = Slope of RS = 4 – 3 2 – 0 Slope of OT = = 2 – 0 4 – 0 The slopes of RSand OTare the same, so RSOT . 2 1 1 2 4 2 EXAMPLE 1 Use a coordinate plane SOLUTION Compare the slopes of opposite sides.

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

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

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

  5. 2. In Example 1, which of the interior angles of quadrilateral ORSTare supplementary angles? Explain your reasoning. 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 for Example 1 GUIDED PRACTICE

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