2. 5.11Properties 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

3. 5.11Properties 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

4. 5.11Properties 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.

5. 5.11Properties 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

6. 5.11Properties of Trapezoids and Kites Example 2 Use properties of isosceles trapezoids 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. L K M N Solution Step 1Find m N. KLMN is an ___________________, so N and ___ are congruent base angles, and isosceles trapezoid K K Step 2 supplementary L Find m L. Because K and L are consecutive interior angles formed by KL intersecting two parallel lines, they are _________________.

7. 5.11Properties of Trapezoids and Kites Example 2 Use properties of isosceles trapezoids 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. L K M N Solution Step 3Find m M. Because M and ___ are a pair of base angles, they are congruent, and L L

8. 5.11Properties of Trapezoids and Kites Checkpoint. Complete the following exercises. 1.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.

9. 5.11Properties of Trapezoids and Kites Checkpoint. Complete the following exercises. 1.Find m C, m A, and m D in the trapezoid shown. A B D C ABCD is an isosceles trapezoid, so base angles are congruent and consecutive interior angles are supplementary.

10. 5.11Properties of Trapezoids and Kites Theorem 5.32 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. If MN is the midsegment of trapezoid ABCD, A D B C M N

11. 5.11Properties of Trapezoids and Kites Example 3 Use the midsegment of a trapezoids Solution In the diagram, MN is the midsegment of trapezoid PQRS. Find MN P S Q R M N Use Theorem 5.32 to find MN. Apply Theorem 5.32 Substitute ___ for PQ and ___ for SR. 16 9 Simplify. 16 in. 9 in.

12. 5.11Properties of Trapezoids and Kites Checkpoint. Complete the following exercises. 2.Find MN in the trapezoid at the right. P S Q R M N 30 ft 12 ft

13. 5.11Properties of Trapezoids and Kites Theorem 5.33 If a quadrilateral is a kite, then its diagonals are _______________. If quadrilateral ABCD is a kite, A D B C perpendicular

14. 5.11Properties 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,

15. 5.11Properties of Trapezoids and Kites Example 4 Use properties of kites Solution By Theorem 5.34, QRST has exactly one pair of __________ opposite angles. Find m T in the kite shown at the right. R Q S T congruent R R Corollary to Theorem 5.16 Substitute. Combine like terms. Solve.

16. 5.11Properties of Trapezoids and Kites Checkpoint. Complete the following exercises. 4.Find m G in the kite shown at the right. G I H J

17. 5.11Properties of Trapezoids and Kites Pg. 339, 5.11 #2-22 even, 23