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Warm Up Solve for x. 1. x 2 + 38 = 3 x 2 – 12 2. 137 + x = 180 3. 4. Find FE .

Warm Up Solve for x. 1. x 2 + 38 = 3 x 2 – 12 2. 137 + x = 180 3. 4. Find FE. 5 or –5. 43. 156. Objectives. Use properties of kites to solve problems. Use properties of trapezoids to solve problems.

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Warm Up Solve for x. 1. x 2 + 38 = 3 x 2 – 12 2. 137 + x = 180 3. 4. Find FE .

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  1. Warm Up Solve for x. 1.x2 + 38 = 3x2 – 12 2. 137 + x = 180 3. 4. Find FE. 5 or –5 43 156

  2. Objectives Use properties of kites to solve problems. Use properties of trapezoids to solve problems.

  3. A kiteis a quadrilateral with exactly two pairs of congruent consecutive sides.

  4. Example 1: Using Properties of Kites In kite ABCD, mDAB = 54°, and mCDF = 52°. Find mBCD. Find mFDA. Find mABC.

  5. A trapezoidis 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 anglesof a trapezoid are two consecutive angles whose common side is a base.

  6. If the legs of a trapezoid are congruent, the trapezoid is an isosceles trapezoid. The following theorems state the properties of an isosceles trapezoid.

  7. Example 2: Using Properties of Isosceles Trapezoids Find mA.

  8. Example 3: Using Properties of Isosceles Trapezoids KB = 21.9m and MF = 32.7. Find FB.

  9. Example 4: Applying Conditions for Isosceles Trapezoids Find the value of a so that PQRS is isosceles.

  10. Example 5: Applying Conditions for Isosceles Trapezoids AD = 12x – 11, and BC = 9x – 2. Find the value of x so that ABCD is isosceles.

  11. Example 6 Find the value of x so that PQST is isosceles.

  12. The midsegment of a trapezoidis the segment whose endpoints are the midpoints of the legs.

  13. Example 7: Finding Lengths Using Midsegments Find EF.

  14. Example 8 Find EH.

  15. 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LHJ 3. mPKL about 191.2 in. 81° 18°

  16. 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. 119° 9.6 18

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