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

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.

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

Isosceles Trapezoid Isosceles Trapezoid- Trapezoid where the legs are congruent

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

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

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

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.

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

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

Midsegment Theorem

Example 10) Find EF.

Example 11) Find EH.