Answer:
Find each measure.
1.
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.
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
the quadrilateral.
The slopes of exactly one pair of opposite sides are
equal. So, they are parallel. Therefore, the
quadrilateral ABCD is a trapezoid.
Use the Distance Formula to find the lengths of the
legs of the trapezoid.
The lengths of the legs are equal. Therefore, ABCD
is an isosceles 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,
Solve for x.
16 = 14.8 + x
1.2 = x
ANSWER:
1.2
CCSS SENSE-MAKING If ABCD is a kite, find
each measure.
6. AB
SOLUTION
* side length^2