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15-2: Trapezoids Objectives: 1. To discover and use properties of trapezoids 2. To find the area of trapezoids Assignment: SpringBoard: • P: 212: 11, 12 • P. 221: 2-4 Purple Geometry Text: • P. 546-9: 6-9, 32, 37-39 • P.733-6: 5, 16, 17, 19, 26, 29 • Almost a Trapezoid Worksheet You will be able to discover and use properties of trapezoids Objective 1 Trapezoids What makes a quadrilateral a trapezoid? Trapezoids A trapezoid is a quadrilateral with exactly one pair of parallel opposite sides. Trapezoid Parts The parallel sides are called bases The non-parallel sides are called legs A trapezoid has two pairs of base angles Example 1 Find the value of x. C B 100 x A D Trapezoid Theorem 1 If a quadrilateral is a trapezoid, then the consecutive angles between the bases are supplementary. C B y x A t r D If ABCD is a trapezoid, then x + y = 180° and r + t = 180°. Midsegment A midsegment of a trapezoid is a segment that connects the midpoints of the legs of a trapezoids. Investigation 1 In this Investigation, you will be using Geometer’s Sketchpad to construct an isosceles trapezoid, and then you will discover some properties about its base angles, diagonals, and midsegment. Trapezoid Midsegment Theorem The midsegment of a trapezoid is parallel to each base and its length is one half the sum of the lengths of the bases. If Example 2 Find the value of x. Example 3 Given: Trapezoid 𝐸𝐹𝐺𝐻 𝑀𝑁 is a midsegment Prove: 𝑀𝑁 ∥ 𝐹𝐺 and 𝑀𝑁 ∥ 𝐸𝐻 𝑀𝑁 = 1 2 𝐹𝐺 + 𝐸𝐻 Isosceles Trapezoid An isosceles trapezoid is a trapezoid with congruent legs. Trapezoid Theorem 2 If a trapezoid is isosceles, then each pair of base angles is congruent. Trapezoid Theorem 3 A trapezoid is isosceles if and only if its diagonals are congruent. T i Example 4 Find the measure of each missing angle. Example 5 Given: Trapezoid 𝐶𝑂𝑅𝐸 𝐶𝑂 ≅ 𝐸𝑅 Prove: 𝐶𝑅 ≅ 𝐸𝑂 Objective 2 You will be able to find the area of trapezoids Investigation 2 Now you will discover a justification for the area formula for trapezoids. Trapezoid Area Example 6 Find the area of the polygon. Example 7 Find the area of the trapezoid. 15-2: Trapezoids Objectives: 1. To discover and use properties of trapezoids 2. To find the area of trapezoids Assignment: SpringBoard: • P: 212: 11, 12 • P. 221: 2-4 Purple Geometry Text: • P. 546-9: 6-9, 32, 37-39 • P.733-6: 5, 16, 17, 19, 26, 29 • Almost a Trapezoid Worksheet