6 6 Trapezoids And Kites

WT + 15 = 20
WT = 5
6-6 Trapezoids and Kites
Find each measure.
1.

ANSWER:
5
COORDINATE GEOMETRY Quadrilateral
ABCD has vertices A (–4, –1), B(–2, 3), C(3, 3), and D(5, –1).
3. Verify that ABCD is a trapezoid.
SOLUTION:
First graph the points on a coordinate grid and draw the trapezoid.

SOLUTION:
The trapezoid ABCD is an isosceles trapezoid. So, each pair of base angles is congruent. Therefore,
ANSWER:
101
2. WT, if ZX = 20 and TY = 15

SOLUTION:
The trapezoid WXYZ is an isosceles trapezoid. So, the diagonals are congruent. Therefore, WY = ZX.
WT + TY = ZX
WT + 15 = 20
WT = 5
ANSWER:
5
COORDINATE GEOMETRY Quadrilateral
ABCD has vertices A (–4, –1), B(–2, 3), C(3, 3), and D(5, –1).
3. Verify that ABCD is a trapezoid.
SOLUTION:
First graph the points on a coordinate grid and draw the trapezoid.

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Use the slope formula to find the slope of the sides of the trapezoid.

Use the slope formula to find the slope of the sides of the trapezoid.

The slopes of exactly one pair of opposite sides are equal. So, they are parallel. Therefore, the quadrilateral ABCD is a trapezoid.
ANSWER:
ABCD is a trapezoid.
4. Determine whether ABCD is an isosceles trapezoid.
Explain.
SOLUTION:
Refer to the graph of the trapezoid.

Use the slope formula to find the slope of the sides of Page 1 the quadrilateral.

The lengths of the legs are equal. Therefore, ABCD is an isosceles trapezoid.

quadrilateral ABCD is a trapezoid.
ANSWER:
6-6 Trapezoids and Kites
ABCD is a trapezoid.
4. Determine whether ABCD is an isosceles trapezoid.
Explain.
SOLUTION:
Refer to the graph of the trapezoid.

ANSWER: isosceles; 5. GRIDDED REPSONSE In the figure, is the midsegment of trapezoid TWRV. Determine the value of x.

SOLUTION:
By the Trapezoid Midsegment Theorem, the midsegment of a trapezoid is parallel to each base and its measure is one half the sum of the lengths of the bases. are the bases and is the midsegment. So,

Use the slope