Name _________________________
Date ______________
Period_________
Section 6-6: Properties of Kites and Trapezoids
Objective: 1. Use properties of kites to solve problems.
2. Use properties of trapezoids to solve problems.
A ____________ is a quadrilateral with exactly two pairs of congruent
consecutive sides. If a quadrilateral is a kite, such as FGHJ,
then it has the following properties.
Properties of Kites
FH  GJ
G  J

The diagonals are ___________________.
Exactly one pair of opposite _________
is congruent.
In kite WXYZ, m∠WXY = 104°, and m∠VYZ = 49°. Find each measure.
1. m∠VZY = ____________
2. m∠VXW = ____________
3. m∠XWZ = ____________
In kite ABCD, m∠DAX = 32°, and m∠XDC = 64°. Find each measure.
4. m∠XDA = ____________
5. m∠ABC = ____________
6. m∠BCD = ____________
In kite PQRS, m∠PQR = 78°, and m∠TRS = 59°. Find each measure.
7. m∠QRT = ____________
8. m∠QPS = ____________
9. m∠PSR = ____________
In kite ABCD, mBCD  98, and mADE  47. Find each measure.
10. mDAE = ______________
12. mABC = ______________
11. mBCE = ______________
A _________________ is a quadrilateral with exactly one pair of parallel sides. If the legs of
a trapezoid are congruent, the trapezoid is an __________________ trapezoid.
Each nonparallel side is
called a leg.
Each ∥ side is
called a base.
Base angles are two
consecutive angles whose
common side is a base.
Isosceles Trapezoid Theorems
• In an isosceles trapezoid, each pair of base angles is ___________________.
• If a trapezoid has one pair of congruent base angles, then it is ____________.
• A trapezoid is isosceles if and only if it’s ________________ are congruent.
14. In trapezoid EFGH, FH  9. Find AG.
13. Find mJ in trapezoid JKLM.
________________________________________
________________________________________
Find each value so that the trapezoid is isosceles.
16. AC  (2z  9), BD  (4z  3). Find the value of z.
15. Find the value of x.
________________________________________
________________________________________
Trapezoid Midsegment Theorem
The __________________ of a trapezoid is the segment
whose endpoints are the midpoints of the legs.
• The midsegment of a trapezoid is parallel to
each base. AB MN and AB LP
• The length of the midsegment is _________-_________
the sum of the length of the bases.
1
AB  (MN  LP)
2
is the
midsegment
of LMNP.
Find each length.
17. KL
18. PQ
________________________________________
19. EF
________________________________________
20. WX
________________________________________
21. x = ________
________________________________________
22. IJ = JL = LG and IK = KM = MH. If GH = 36, then
LM = ___________ and JK = __________.
23. x = _______, y = ________
24. x = ________, y = ________
137°
78°
x°
x°
41°
22°
y°
y°