1. Holt Geometry 6-6 Properties of Kites and Trapezoids Warm Up Solve for x. 1. x 2 + 38 = 3x 2 – 12 2. 137 + x = 180 3. 4. Find FE.

2. Holt Geometry 6-6 Properties of Kites and Trapezoids Use properties of kites to solve problems. Use properties of trapezoids to solve problems. Objectives

3. Holt Geometry 6-6 Properties of Kites and Trapezoids A kite is a quadrilateral with exactly two pairs of congruent consecutive sides.

4. Holt Geometry 6-6 Properties of Kites and Trapezoids

5. Holt Geometry 6-6 Properties of Kites and Trapezoids Lucy is framing a kite with wooden dowels. She uses two dowels that measure 18 cm, one dowel that measures 30 cm, and two dowels that measure 27 cm. To complete the kite, she needs a dowel to place along. She has a dowel that is 36 cm long. About how much wood will she have left after cutting the last dowel?

6. Holt Geometry 6-6 Properties of Kites and Trapezoids In kite ABCD, mDAB = 54°, and mCDF = 52°. Find mBCD.

7. Holt Geometry 6-6 Properties of Kites and Trapezoids In kite ABCD, mDAB = 54°, and mCDF = 52°. Find mFDA.

8. Holt Geometry 6-6 Properties of Kites and Trapezoids In kite PQRS, mPQR = 78°, and mTRS = 59°. Find mQRT.

9. Holt Geometry 6-6 Properties of Kites and Trapezoids In kite PQRS, mPQR = 78°, and mTRS = 59°. Find mQPS.

10. Holt Geometry 6-6 Properties of Kites and Trapezoids A trapezoid is a quadrilateral with exactly one pair of parallel sides. Each of the parallel sides is called a base. The nonparallel sides are called legs. Base angles of a trapezoid are two consecutive angles whose common side is a base.

11. Holt Geometry 6-6 Properties of Kites and Trapezoids If the legs of a trapezoid are congruent, the trapezoid is an isosceles trapezoid. The following theorems state the properties of an isosceles trapezoid.

12. Holt Geometry 6-6 Properties of Kites and Trapezoids

13. Holt Geometry 6-6 Properties of Kites and Trapezoids Find mA.

14. Holt Geometry 6-6 Properties of Kites and Trapezoids KB = 21.9m and MF = 32.7. Find FB.

15. Holt Geometry 6-6 Properties of Kites and Trapezoids Find mF.

16. Holt Geometry 6-6 Properties of Kites and Trapezoids JN = 10.6, and NL = 14.8. Find KM.

17. Holt Geometry 6-6 Properties of Kites and Trapezoids Find the value of a so that PQRS is isosceles.

18. Holt Geometry 6-6 Properties of Kites and Trapezoids AD = 12x – 11, and BC = 9x – 2. Find the value of x so that ABCD is isosceles.

19. Holt Geometry 6-6 Properties of Kites and Trapezoids Find the value of x so that PQST is isosceles.

20. Holt Geometry 6-6 Properties of Kites and Trapezoids The midsegment of a trapezoid is the segment whose endpoints are the midpoints of the legs. In Lesson 5-1, you studied the Triangle Midsegment Theorem. The Trapezoid Midsegment Theorem is similar to it.

21. Holt Geometry 6-6 Properties of Kites and Trapezoids

22. Holt Geometry 6-6 Properties of Kites and Trapezoids Find EF.

23. Holt Geometry 6-6 Properties of Kites and Trapezoids Find EH.

24. Holt Geometry 6-6 Properties of Kites and Trapezoids 1. Erin is making a kite based on the pattern below. About how much binding does Erin need to cover the edges of the kite? In kite HJKL, mKLP = 72°, and mHJP = 49.5°. Find each measure. 2. mLHJ3. mPKL

25. Holt Geometry 6-6 Properties of Kites and Trapezoids Use the diagram for Items 4 and 5. 4. mWZY = 61°. Find mWXY. 5. XV = 4.6, and WY = 14.2. Find VZ. 6. Find LP.

26. Holt Geometry 6-6 Properties of Kites and Trapezoids Home Work Pg# 432 4,6,8,12,14,16, 18,22,23,24,25,2 8,32,46,56