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

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

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.

5.11Properties 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

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 _________________.

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

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.

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.

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

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 Simplify. 16 in. 9 in.

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

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

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,

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.

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

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