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5.11

5.11. Properties of Trapezoids and Kites. 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. Use a coordinate plane. Example 1. Show that CDEF is a trapezoid. Solution. Compare the slopes of the opposite sides.

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5.11

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  1. 5.11 Properties of Trapezoids and Kites 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. Use a coordinate plane Example 1 Show that CDEF is a trapezoid. Solution Compare the slopes of the opposite sides. not parallel Because quadrilateral CDEF has exactly one pair of _______________, it is a trapezoid. parallel sides

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

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

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

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

  6. 5.11 Properties of Trapezoids and Kites 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 M N K Find m M. Because M and ___ are a pair of base angles, they are congruent, and Use properties of isosceles trapezoids Example 2 Solution L Step 3 L

  7. 5.11 Properties of Trapezoids and Kites 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. Checkpoint. Complete the following exercises. • In Example 1, suppose the coordinates of E are (7, 5). What type of quadrilateral is CDEF? Explain. Therefore the opposite sides are parallel and CDEF is a parallelogram.

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

  9. 5.11 Properties of Trapezoids and Kites A B N M C D 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,

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

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

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

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

  14. 5.11 Properties of Trapezoids and Kites Find m T in the kite shown at the right. Q R S T Use properties of kites Example 4 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. 5.11 Properties of Trapezoids and Kites • Find m G in the kite shown at the right. G H I J Checkpoint. Complete the following exercises.

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

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