# 6.6 properties of kites and trapezoids

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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. - PowerPoint PPT Presentation

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6.6 Properties of Kites and Trapezoids

6.6 Properties of Kites and Trapezoids1KiteKite- a quadrilateral with exactly two pairs of congruent consecutive sides.

2KiteProperties of KitesDiagonals are perpendicular

Exactly one pair of opposite angles are congruent3ExampleIn kite ABCD, mDAB = 54, and mCDF = 52.

a) Find mBCD.

b) Find mABC.

c) Find mFDA.

4Example2) In kite PQRS, mPQR = 78, and mTRS = 59. a) Find mQRT.

b) Find mQPS.

c) Find each mPSR.

5TrapezoidTrapezoid- exactly one pair of parallel sidesBase- parallel sidesLegs- nonparallel sidesBase angles- two consecutive angles whose common side is a base

6Isosceles TrapezoidIsosceles Trapezoid- Trapezoid where the legs are congruent7Isosceles TrapezoidProperties of Isosceles TrapezoidsBase angles are congruent

One pair of congruent sides (legs)

Diagonals are congruent8Example3) Find mA.

4) KB = 21.9 and MF = 32.7. Find FB.

9Example5) Find mF.

6) JN = 10.6, and NL = 14.8. Find KM.

10Example7) 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.

11Example9) Find the value of x so that PQST is isosceles.

12MidsegmentMidsegment of a trapezoid- a segment whose endpoints are the midpoints of the legs

13Midsegment Theorem

14Example10) Find EF.

15Example11) Find EH.

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