1. Holt McDougal 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 McDougal Geometry 6-6 Properties of Kites and Trapezoids

3. Holt McDougal Geometry 6-6 Properties of Kites and Trapezoids Kites and trapezoids are quadrilaterals that do not fall under the category of parallelograms.

4. Holt McDougal Geometry 6-6 Properties of Kites and Trapezoids A kite is a quadrilateral with exactly two pairs of congruent consecutive sides. Kite Properties: 1.Diagonals are perpendicular. 2.Only the pair of non-vertex angles are congruent. 3.Diagonals only bisect the vertex angles. 4.Only the diagonal through the non-vertex angles is bisected.

5. Holt McDougal 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 McDougal Geometry 6-6 Properties of Kites and Trapezoids In kite ABCD, mDAB = 54°, and mCDF = 52°. 1.Find mFDA. 2.Find mABC. 3. Find mBCD.

7. Holt McDougal Geometry 6-6 Properties of Kites and Trapezoids In kite PQRS, mPQR = 78°, and mTRS = 59°. 1.Find mQRT. 2.2. Find mQPS. 3.Find mPSR.

8. Holt McDougal 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.

9. Holt McDougal Geometry 6-6 Properties of Kites and Trapezoids Isosceles Trapezoid The bases are parallel. The legs are congruent. Both pairs of base angles are congruent. Leg angles add up to 180 degrees. The diagonals are congruent. Diagonals do not bisect each other.

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

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

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

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

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

15. Holt McDougal 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.

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

17. Holt McDougal Geometry 6-6 Properties of Kites and Trapezoids The midsegment of a trapezoid is the segment whose endpoints are the midpoints of the legs.

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

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

20. Holt McDougal Geometry 6-6 Properties of Kites and Trapezoids WXYZ is an isosceles trapezoid with bases WZ and XY and median MN. 1.Find MN if WZ = 11 and XY = 3. 2. Find m ∠ XMN if m ∠ WZN = 78.

21. Holt McDougal Geometry 6-6 Properties of Kites and Trapezoids 3. If MN = 10 and WZ = 14. Find XY. 4. What is the value of x if m ∠ MWZ = 15x – 5 and m ∠ WZN = 90 – 4x?

22. Holt McDougal Geometry 6-6 Properties of Kites and Trapezoids 5. If m ∠ XWZ = 2x – 7 and m ∠ XYZ = 117. Find x. 6. If MN= 60, XY = 4x – 1, and WZ = 6x + 11. Find x.

23. Holt McDougal Geometry 6-6 Properties of Kites and Trapezoids 7. If MN = 10x + 3, WZ = 11 and XY = 8x + 19. Find x. 8. IF MN = 2x + 1, XY = 8 and WZ = 3x – 3. Find x.

24. Holt McDougal Geometry 6-6 Properties of Kites and Trapezoids Lesson Quiz: Part I 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 McDougal Geometry 6-6 Properties of Kites and Trapezoids Lesson Quiz: Part II 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.