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Exploring Trapezoids: Slope Analysis & Interior Angles Explanation

Learn how to identify a trapezoid using slope analysis and discover interior angles of quadrilaterals using a coordinate plane. Practice questions included for better understanding.

brittany-peters
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Exploring Trapezoids: Slope Analysis & Interior Angles Explanation

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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. 2. In Example 1, which of the interior angles of quadrilateral ORSTare supplementary angles? Explain your reasoning. Parallelogram; opposite pairs of sides are parallel. ANSWER O and R , T and S;Consecutive Interior Angles Theorem ANSWER 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.

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