EXAMPLE 1 Use a coordinate plane Show that ORST is a trapezoid.

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Presentation transcript:

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 .

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

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 .

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.

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