You used properties of special parallelograms.

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Date: Sec 8-5 Concept: Trapezoids and Kites

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Presentation transcript:

You used properties of special parallelograms. Apply properties of trapezoids. Apply properties of kites. Then/Now

midsegment of a trapezoid kite bases legs of a trapezoid base angles isosceles trapezoid midsegment of a trapezoid kite Vocabulary

Concept 1

Isosceles 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. A quadrilateral is a trapezoid if exactly one pair of opposite sides are parallel. Use the Slope Formula. Example 2

slope of slope of slope of Isosceles Trapezoids and Coordinate Geometry slope of slope of slope of Answer: Exactly one pair of opposite sides are parallel, So, ABCD is a trapezoid. Example 2

Use the Distance Formula to show that the legs are congruent. Isosceles Trapezoids and Coordinate Geometry Use the Distance Formula to show that the legs are congruent. Answer: Since the legs are not congruent, ABCD is not an isosceles trapezoid. Example 2

A. trapezoid; not isosceles B. trapezoid; isosceles C. not a trapezoid 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. A. trapezoid; not isosceles B. trapezoid; isosceles C. not a trapezoid D. cannot be determined Example 2

Concept 3

Midsegment of a Trapezoid In the figure, MN is the midsegment of trapezoid FGJK. What is the value of x? Example 3

Trapezoid Midsegment Theorem Midsegment of a Trapezoid Read the Test Item You are given the measure of the midsegment of a trapezoid and the measures of one of its bases. You are asked to find the measure of the other base. Solve the Test Item Trapezoid Midsegment Theorem Substitution Example 3

Subtract 20 from each side. Midsegment of a Trapezoid Multiply each side by 2. Subtract 20 from each side. Answer: x = 40 Example 3

WXYZ is an isosceles trapezoid with median Find XY if JK = 18 and WZ = 25. A. XY = 32 B. XY = 25 C. XY = 21.5 D. XY = 11 Example 3

Concept 4