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6.6 Properties of Kites and Trapezoids

6.6 Properties of Kites and Trapezoids. Kite. Kite- a quadrilateral with exactly two pairs of congruent consecutive sides. Kite. Properties of Kites Diagonals are perpendicular Exactly one pair of opposite angles are congruent. Example.

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6.6 Properties of Kites and Trapezoids

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  1. 6.6 Properties of Kites and Trapezoids

  2. Kite • Kite- a quadrilateral with exactly two pairs of congruent consecutive sides.

  3. Kite • Properties of Kites • Diagonals are perpendicular • Exactly one pair of opposite angles are congruent

  4. Example • In kite ABCD, mDAB = 54°, and mCDF = 52°. a) Find mBCD. b) Find mABC. c) Find mFDA.

  5. Example 2) In kite PQRS, mPQR= 78°, and mTRS= 59°. a) Find mQRT. b) Find mQPS. c) Find each mPSR.

  6. Trapezoid • Trapezoid- exactly one pair of parallel sides • Base- parallel sides • Legs- nonparallel sides • Base angles- two consecutive angles whose common side is a base

  7. Isosceles Trapezoid • Isosceles Trapezoid- Trapezoid where the legs are congruent

  8. Isosceles Trapezoid • Properties of Isosceles Trapezoids • Base angles are congruent • One pair of congruent sides (legs) • Diagonals are congruent

  9. Example 3) Find mA. 4) KB = 21.9 and MF = 32.7. Find FB.

  10. Example 5) Find mF. 6) JN = 10.6, and NL = 14.8. Find KM.

  11. Example 7) Find the value of a so that PQRS is isosceles. 8) AD = 12x – 11, and BC = 9x – 2. Find the value of x so that ABCD is isosceles.

  12. Example 9) Find the value of x so that PQST is isosceles.

  13. Midsegment • Midsegment of a trapezoid- a segment whose endpoints are the midpoints of the legs

  14. Midsegment Theorem

  15. Example 10) Find EF.

  16. Example 11) Find EH.

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