then/now you used properties of special parallelograms. apply properties of trapezoids. apply...
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You used properties of special parallelograms.
• Apply properties of trapezoids.
• Apply properties of kites.
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• trapezoid
• bases
• legs of a trapezoid
• base angles
• isosceles trapezoid
• midsegment of a trapezoid
• kite
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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.
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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.
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Isosceles Trapezoids and Coordinate Geometry
Answer: Since the legs are not congruent, ABCD is not an isosceles trapezoid.
Use the Distance Formula to show that the legs are congruent.
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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
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In the figure, MN is the midsegment of trapezoid FGJK. What is the value of x?
Midsegment of a Trapezoid
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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 MidsegmentTheorem
Substitution
Midsegment of a Trapezoid
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Multiply each side by 2.
Subtract 20 from each side.
Answer: x = 40
Midsegment of a Trapezoid
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A. XY = 32
B. XY = 25
C. XY = 21.5
D. XY = 11
WXYZ is an isosceles trapezoid with medianFind XY if JK = 18 and WZ = 25.
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