1. A kite is a quadrilateral with exactly two pairs of congruent consecutive sides.

2. Example 1:
Lucy is framing a kite with wooden dowels. She uses two dowels that measure 18 cm, one dowel that measures 30 cm, and two dowels that measure 27 cm. To complete the kite, she needs a dowel to place along . She has a dowel that is 36 cm long. About how much wood will she have left after cutting the last dowel? N
36 – 32.4  3.6 cm left

3. In kite ABCD, mDAB = 54°, and mCDF = 52°. Find mBCD.
Example 2A:
Kite  cons. sides 
∆BCD is isos.
2  sides isos. ∆
CBF  CDF
isos. ∆ base s 
mCBF = mCDF
Def. of   s
mBCD + mCBF + mCDF = 180°
Polygon  Sum Thm.
mBCD + mCBF + mCDF = 180°
mBCD + 52° + 52° = 180°
mBCD = 76°

4. A trapezoid is a quadrilateral with exactly one pair of parallel sides
A trapezoid is a quadrilateral with exactly one pair of parallel sides. Each of the parallel sides is called a base. The nonparallel sides are called legs. Base angles of a trapezoid are two consecutive angles whose common side is a base.

5. If the legs of a trapezoid are congruent, the trapezoid is an isosceles trapezoid. The following theorems state the properties of an isosceles trapezoid.

6. Example 3a
Find mF.
mF + mE = 180°
Same-Side Int. s Thm.
E  H
Isos. trap. s base 
mE = mH
Def. of  s
mF + 49° = 180°
Substitute 49 for mE.
mF = 131°
Simplify.

7. Example 3b
JN = 10.6, and NL = Find KM.
Isos. trap. s base 
KM = JL
Def. of  segs.
JL = JN + NL
Segment Add Postulate
KM = JN + NL
Substitute.
KM = = 25.4
Substitute and simplify.

8. Example 4
Find the value of x so that PQST is isosceles.
Trap. with pair base s   isosc. trap.
Q  S
mQ = mS
Def. of  s
Substitute 2x for mQ and 4x2 – 13 for mS.
2x = 4x2 – 13
Subtract 2x2 and add 13 to both sides.
32 = 2x2
Divide by 2 and simplify.
x = 4 or x = –4

9. The midsegment of a trapezoid is the segment whose endpoints are the midpoints of the legs. In Lesson 5-1, you studied the Triangle Midsegment Theorem. The Trapezoid Midsegment Theorem is similar to it.

10. Example 5A
Find EF.
Trap. Midsegment Thm.
Substitute the given values.
EF = 10.75
Solve.

11. Geom 6.6 Kites and Trapezoids
Example 5B
Find EH.
Trap. Midsegment Thm. 1
16.5 = (25 + EH) 2
Substitute the given values.
Simplify.
33 = 25 + EH
Multiply both sides by 2.
13 = EH
Subtract 25 from both sides.