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

Example1) In kite ABCD, mDAB = 54°, and

mCDF = 52°.

a) Find mBCD.

b) Find mABC.

c) Find mFDA.

Example2) In kite PQRS, mPQR = 78°, and

mTRS = 59°.

a) Find mQRT.

b) Find mQPS.

c) Find each mPSR.

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

Example3) Find mA.

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

Example5) Find mF.

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

Example7) 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.

Example9) 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

Example10) Find EF.

Example11) Find EH.