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6-6 Properties of Kites and Trapezoids
Warm Up
Solve for x.
1. x2 + 38 = 3x2 – 12 5 or –5
2. 137 + x = 180
43
3.
156
4. Find FE.
Holt Geometry
6-6 Properties of Kites and Trapezoids
6-6
Holt
Geometry
Holt
Geometry
Properties of Kites
and Trapezoids
6-6 Properties of Kites and Trapezoids
A kite is a quadrilateral with exactly two pairs of
congruent consecutive sides.
Holt Geometry
6-6 Properties of Kites and Trapezoids
Holt Geometry
6-6 Properties of Kites and Trapezoids
Example 2A: Using Properties of Kites
In kite ABCD, mDAB = 54°, and
mCDF = 52°. Find mBCD.
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.
Holt Geometry
6-6 Properties of Kites and Trapezoids
Example 2A Continued
mBCD + mCBF + mCDF = 180°
Substitute mCDF
mBCD + mCBF + mCDF = 180°
for mCBF.
Substitute 52 for
mBCD + 52° + 52° = 180°
mCBF.
mBCD = 76°
Holt Geometry
Subtract 104
from both sides.
6-6 Properties of Kites and Trapezoids
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.
Holt Geometry
6-6 Properties of Kites and Trapezoids
If the legs of a trapezoid are congruent, the trapezoid
is an isosceles trapezoid.
Holt Geometry
6-6 Properties of Kites and Trapezoids
Holt Geometry
6-6 Properties of Kites and Trapezoids
Example 3A: Using Properties of Isosceles
Trapezoids
Find mA.
mC + mB = 180°
100 + mB = 180
Holt Geometry
Same-Side Int. s Thm.
Substitute 100 for mC.
mB = 80°
A  B
Subtract 100 from both sides.
Isos. trap. s base 
mA = mB
Def. of  s
mA = 80°
Substitute 80 for mB
6-6 Properties of Kites and Trapezoids
Example 3B: Using Properties of Isosceles
Trapezoids
KB = 21.9m and MF = 32.7.
Find FB.
Isos.  trap. s base 
KJ = FM
Def. of  segs.
KJ = 32.7 Substitute 32.7 for FM.
KB + BJ = KJ
Seg. Add. Post.
21.9 + BJ = 32.7 Substitute 21.9 for KB and 32.7 for KJ.
BJ = 10.8 Subtract 21.9 from both sides.
Holt Geometry
6-6 Properties of Kites and Trapezoids
Check It Out! Example 3b
JN = 10.6, and NL = 14.8.
Find KM.
Isos. trap. s base 
KM = JL
JL = JN + NL
Def. of  segs.
KM = JN + NL
Substitute.
Segment Add Postulate
KM = 10.6 + 14.8 = 25.4 Substitute and simplify.
Holt Geometry
6-6 Properties of Kites and Trapezoids
Example 4A: Applying Conditions for Isosceles
Trapezoids
Find the value of a so that PQRS
is isosceles.
Trap. with pair base
s   isosc. trap.
S  P
mS = mP
2a2
– 54 =
a2
a2
Substitute 2a2 – 54 for mS and
+ 27 2
a + 27 for mP.
= 81
a = 9 or a = –9
Holt Geometry
Def. of  s
Subtract a2 from both sides and add
54 to both sides.
Find the square root of both sides.
6-6 Properties of Kites and Trapezoids
Example 4B: Applying Conditions for Isosceles
Trapezoids
AD = 12x – 11, and BC = 9x – 2. Find
the value of x so that ABCD is
isosceles.
Diags.   isosc. trap.
AD = BC
Def. of  segs.
Substitute 12x – 11 for AD and
12x – 11 = 9x – 2 9x – 2 for BC.
3x = 9
x=3
Holt Geometry
Subtract 9x from both sides and add
11 to both sides.
Divide both sides by 3.
6-6 Properties of Kites and Trapezoids
The midsegment of a trapezoid is the segment
whose endpoints are the midpoints of the legs.
Holt Geometry
6-6 Properties of Kites and Trapezoids
Holt Geometry
6-6 Properties of Kites and Trapezoids
Example 5: Finding Lengths Using Midsegments
Find EF.
Trap. Midsegment Thm.
Substitute the given values.
EF = 10.75
Holt Geometry
Solve.
6-6 Properties of Kites and Trapezoids
Check It Out! Example 5
Find EH.
Trap. Midsegment Thm.
1
16.5 = 2 (25 + EH) Substitute the given values.
Simplify.
33 = 25 + EH
Multiply both sides by 2.
13 = EH
Subtract 25 from both sides.
Holt Geometry
6-6 Properties of Kites and Trapezoids
Lesson Quiz: Part I
1. Erin is making a kite based on
the pattern below. About how
much binding does Erin need to
cover the edges of the kite?
about 191.2 in.
In kite HJKL, mKLP = 72°,
and mHJP = 49.5°. Find each
measure.
2. mLHJ
Holt Geometry
81°
3. mPKL
18°
6-6 Properties of Kites and Trapezoids
Lesson Quiz: Part II
Use the diagram for Items 4 and 5.
4. mWZY = 61°. Find mWXY.
119°
5. XV = 4.6, and WY = 14.2. Find VZ.
9.6
6. Find LP.
18
Holt Geometry