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

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

3. Concept 1

4. 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

5. 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

6. 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

7. 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

8. Concept 3

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

10. 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

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

12. 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

13. Concept 4