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 PresentationTRANSCRIPT
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.