1. Properties of Trapezoids and Kites
5.11
Properties of Trapezoids and Kites
Example 1
Use a coordinate plane
Show that CDEF is a trapezoid.
Solution
Compare the slopes of the opposite sides.
The slopes of DE and CF are the same, so DE ___ CF.
The slopes of EF and CD are not the same, so EF is ______________ to CD.
not parallel
Because quadrilateral CDEF has exactly one pair of _______________, it is a trapezoid.
parallel sides

2. Properties of Trapezoids and Kites
5.11
Properties of Trapezoids and Kites
Theorem 5.29
If a trapezoid is isosceles, then each pair of base angles is _____________.
congruent A D B C
If trapezoid ABCD is isosceles, then

3. Properties of Trapezoids and Kites
5.11
Properties of Trapezoids and Kites
Theorem 5.30
If a trapezoid has a pair of congruent ___________, then it is an isosceles trapezoid.
base angles A D B C
then trapezoid ABCD is isosceles.

4. Properties of Trapezoids and Kites
5.11
Properties of Trapezoids and Kites
Theorem 5.31
A trapezoid is isosceles if and only if its diagonals are __________.
congruent A D B C
Trapezoid ABCD is isosceles if and only if

5. Properties of Trapezoids and Kites
5.11
Properties of Trapezoids and Kites
Example 2
Use properties of isosceles trapezoids L K M N
Kitchen A shelf fitting into a cupboard in the corner of a kitchen is an isosceles trapezoid. Find m N, m L, and m M.
Solution
Step 1
Find m N. KLMN is an ___________________, so N and ___ are congruent base angles, and
isosceles trapezoid K K
Step 2
Find m L. Because K and L are consecutive interior angles formed by KL intersecting two parallel lines, they are _________________.
supplementary L

6. Properties of Trapezoids and Kites
5.11
Properties of Trapezoids and Kites
Example 2
Use properties of isosceles trapezoids L K M N
Kitchen A shelf fitting into a cupboard in the corner of a kitchen is an isosceles trapezoid. Find m N, m L, and m M.
Solution
Step 3
Find m M. Because M and ___ are a pair of base angles, they are congruent, and L L

7. Properties of Trapezoids and Kites
5.11
Properties of Trapezoids and Kites
Checkpoint. Complete the following exercises.
In Example 1, suppose the coordinates of E are (7, 5). What type of quadrilateral is CDEF? Explain.
The slopes of DE and CF are the same, so DE ___ CF.
The slopes of EF and CD are the same, so EF ___ CD.
Because the slopes of DE and CD are not the opposite reciprocals of each other, they are not perpendicular.
Therefore the opposite sides are parallel and CDEF is a parallelogram.

8. Properties of Trapezoids and Kites
5.11
Properties of Trapezoids and Kites
Checkpoint. Complete the following exercises. A B D C
Find m C, m A, and m D in the trapezoid shown.
ABCD is an isosceles trapezoid, so base angles are congruent and consecutive interior angles are supplementary.

9. Properties of Trapezoids and Kites
5.11
Properties of Trapezoids and Kites
Theorem Midsegment Theorem of Trapezoids
The midsegment of a trapezoid is parallel to each base and its length is one half the sum of the lengths of the bases. A D B C M N
If MN is the midsegment of trapezoid ABCD,

10. Properties of Trapezoids and Kites
5.11
Properties of Trapezoids and Kites
Example 3
Use the midsegment of a trapezoids
16 in.
In the diagram, MN is the midsegment of trapezoid PQRS. Find MN P S Q R M N
Solution
Use Theorem 5.32 to find MN.
9 in.
Apply Theorem 5.32
Substitute ___ for PQ and ___ for SR. 16 9
Simplify.

11. Properties of Trapezoids and Kites
5.11
Properties of Trapezoids and Kites
Checkpoint. Complete the following exercises. P S Q R M N
Find MN in the trapezoid at the right.
12 ft
30 ft

12. Properties of Trapezoids and Kites
5.11
Properties of Trapezoids and Kites
Theorem 5.33
If a quadrilateral is a kite, then its diagonals are _______________.
perpendicular A D B C
If quadrilateral ABCD is a kite,

13. Properties of Trapezoids and Kites
5.11
Properties of Trapezoids and Kites
Theorem 5.34
If a quadrilateral is a kite, then exactly one pair of opposite angles are congruent. A D B C
If quadrilateral ABCD is a kite and BC BA,

14. Properties of Trapezoids and Kites
5.11
Properties of Trapezoids and Kites
Example 4
Use properties of kites R Q S T
Find m T in the kite shown at the right.
Solution
By Theorem 5.34, QRST has exactly one pair of __________ opposite angles.
congruent R R
Corollary to Theorem 5.16
Substitute.
Combine like terms.
Solve.

15. Properties of Trapezoids and Kites
5.11
Properties of Trapezoids and Kites
Checkpoint. Complete the following exercises.
Find m G in the kite shown at the right. G I H J

16. Properties of Trapezoids and Kites
5.11
Properties of Trapezoids and Kites
Pg. 339, 5.11 #2-22 even, 23