6.6 Notes Trapezoids and Kites

Learning Goal: I can apply the properties of trapezoids and kites to solve problems.

Trapezoids

Trapezoid: Isosceles Trapezoid:

Example 1

Each side of the basket shown is an isosceles trapezoid. If mJML = 130, KN = 6.7 feet, and LN = 3.6 feet, find mMJK.

Example 2

Find 𝑚 ∠ 𝑇 Find 𝑚 ∠ 𝑍 Example 3 Each side of the basket shown is an isosceles trapezoid. If mJML = 130, KN = 6.7 feet, and JL is 10.3 feet, find MN.

Trapezoids and Coordinate Geometry

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. (HINT: A quadrilateral is a trapezoid if exactly one pair of opposite sides are parallel. Use the Slope Formula.)

Midsegments of Trapezoids

The Formula

Example 4 a) In the figure, MN is the midsegment of trapezoid FGJK. What is the value of x? b) WXYZ is an isosceles trapezoid with midsegment JK. Find XY if JK = 18 and WZ = 25.

Kites

Kite:

Example 5 If WXYZ is a kite, find mXYZ.

Example 6 If BCDE is a kite, find mCDE. Example 7 If MNPQ is a kite, find m MRQ.