Geometry Unit 6 Note Sheets

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6.6 Trapezoids and Kites Notes

Use Properties of Isosceles Trapezoids Example 1: A. BASKET Each side of the basket shown is an isosceles trapezoid. If m�JML = 130, KN = 6.7 feet, and MN = 3.6 feet, find m�MJK. Example 1: B. BASKET Each side of the basket shown is an isosceles trapezoid. If m�JML = 130, KN = 6.7 feet, and MN = 3.6 feet, find JL.

Geometry Unit 6 Note Sheets

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Guided Practice 1: A. Each side of the basket shown is an isosceles trapezoid. If m�FGH = 124, FI = 9.8 feet, and IG = 4.3 feet, find m�EFG. Guided Practice 1: B. Each side of the basket shown is an isosceles trapezoid. If m�FGH = 124, FI = 9.8 feet, and EG = 14.1 feet, find IH. Example 2: Quadrilateral ABCD has vertices A(5, 1), B(–3, –1), C(–2, 3), and D(2, 4). Show that ABCD is a trapezoid and determine whether it is an isosceles trapezoid. Guided Practice 2: Quadrilateral QRST has vertices Q(–1, 0), R(2, 2), S(5, 0), and T(–1, –4). Determine whether QRST is a trapezoid and if so, determine whether it is an isosceles trapezoid.

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Example 3: In the figure, MN is the midsegment of trapezoid FGJK. What is the value of x? Guided Practice 3: WXYZ is an isosceles trapezoid with median Find XY if JK = 18 and WZ = 25.

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More examples: The speaker shown is an isosceles trapezoid. If 𝑚∠𝐹𝐽𝐻 = 85, 𝐹𝐾 = 8 𝑖𝑛𝑐ℎ𝑒𝑠, and 𝐽𝐺 = 19 𝑖𝑛𝑐ℎ𝑒𝑠, find each measure. 1. 𝑚∠𝐹𝐺𝐻 2. 𝐾𝐻 Each side of the basket shown is an isosceles trapezoid. If 𝑚∠𝐽𝑀𝐿 = 130, 𝐾𝑁 = 6.7 𝑓𝑒𝑒𝑡, and 𝑀𝑁 = 3.6 𝑓𝑒𝑒𝑡, find each measure. 3. 𝑚∠𝑀𝐽𝐾 4. 𝐽𝐿 5. In the figure 𝐿𝐻 is the midsegment of trapezoid 𝐹𝐺𝐽𝐾. What is the value of x?

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6. Quadrilateral ABCD has vertices 𝐴(−3, 4), 𝐵(2, 5), 𝐶(3, 3), and 𝐷(−1, 0). Show that ABCD is a trapezoid and determine whether it is an isosceles trapezoid. 7. Quadrilateral ABCD has vertices 𝐴(5, 1), 𝐵(−3, −1), 𝐶(−2, 3), and 𝐷(2, 4). Show that ABCD is a trapezoid and determine whether it is an isosceles trapezoid.

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Example 4: A. If WXYZ is a kite, find m�XYZ. Example 4: B. If MNPQ is a kite, find NP. Guided Practice 4: A. If BCDE is a kite, find m�CDE. Guided Practice 4: B. If JKLM is a kite, find KL. More examples: 9. If 𝐹𝐺𝐻𝐽 is a kite, find 𝑚∠𝐺𝐹𝐽. 10. If 𝑊𝑋𝑌𝑍 is a kite, find 𝑍𝑌.