Warm Up

1
Use Properties of Trapezoids and Kites
Warm Up
Lesson Presentation
Lesson Quiz
2
Warm-Up
Use the figure to answer the questions.
1. What are the values of x and y?
3
Example 1
Show that ORST is a trapezoid.
SOLUTION
Compare the slopes of opposite sides.
4
Example 1
5
Guided Practice
1. WHAT IF? In Example 1, suppose the
coordinates of point S are (4, 5). What type of
quadrilateral is ORST? Explain.
6
Example 2
SOLUTION
7
Example 2
STEP 2
8
Example 3
Apply Theorem 8.17.
Substitute 12 for PQ and 28 for XU.
20
Simplify.
The length MN is 20 inches.
9
Guided Practice
In Exercises 3 and 4, use the diagram of
trapezoid EFGH.
3. If EG FH, is trapezoid EFGH isosceles?
Explain.
10
Guided Practice
In Exercises 3 and 4, use the diagram of
trapezoid EFGH.
11
Guided Practice
12
Example 4
Find m D in the kite shown at the right.
SOLUTION
13
Example 4
Corollary to Theorem 8.1
Combine like terms.
14
Guided Practice
6. In a kite, the measures of the angles are
3x, 75, 90, and 120. Find the value of x.
What are the measures of the angles that are
congruent?
15
Lesson Quiz
16
Lesson Quiz
17
Lesson Quiz
Use the figure to find the indicated measures.
4. If XO 2, OZ 2, YO 6, and OW 8, find
the lengths of the sides of the kite.