Properties
of
Kites
6-6
of Kites and Trapezoids
6-6 Properties
and Trapezoids
Warm Up
Lesson Presentation
Lesson Quiz
Holt
Geometry
Holt
Geometry
6-6 Properties of Kites and Trapezoids
Do Now
Solve for x.
1. x2 + 38 = 3x2 – 12
2. 137 + x = 180
3.
4. Find FE.
Holt Geometry
6-6 Properties of Kites and Trapezoids
Objectives
TSW use properties of kites and
trapezoids to solve problems.
Holt Geometry
6-6 Properties of Kites and Trapezoids
Vocabulary
kite
trapezoid
base of a trapezoid
leg of a trapezoid
base angle of a trapezoid
isosceles trapezoid
midsegment of a trapezoid
Holt Geometry
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 1: Problem-Solving Application
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?
Holt Geometry
6-6 Properties of Kites and Trapezoids
Holt Geometry
6-6 Properties of Kites and Trapezoids
Example 2
What if...? Daryl is going to make
a kite by doubling all the measures
in the kite. What is the total
amount of binding needed to cover
the edges of his kite? How many
packages of binding must Daryl
buy?
Holt Geometry
6-6 Properties of Kites and Trapezoids
Holt Geometry
6-6 Properties of Kites and Trapezoids
Example 3: Using Properties of Kites
In kite ABCD, mDAB = 54°, and
mCDF = 52°. Find mBCD.
Holt Geometry
6-6 Properties of Kites and Trapezoids
Example 3.5: Using Properties of Kites
In kite ABCD, mDAB = 54°, and
mCDF = 52°. Find mABC.
Holt Geometry
6-6 Properties of Kites and Trapezoids
Example 4: Using Properties of Kites
In kite ABCD, mDAB = 54°, and
mCDF = 52°. Find mFDA.
Holt Geometry
6-6 Properties of Kites and Trapezoids
Example 5
In kite PQRS, mPQR = 78°,
and mTRS = 59°. Find
mQRT.
Holt Geometry
6-6 Properties of Kites and Trapezoids
Example 5a
In kite PQRS, mPQR = 78°,
and mTRS = 59°. Find
mQPS.
Holt Geometry
6-6 Properties of Kites and Trapezoids
Example 5b
In kite PQRS, mPQR = 78°,
and mTRS = 59°. Find each
mPSR.
Holt Geometry
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. The following theorems
state the properties of an isosceles trapezoid.
Holt Geometry
6-6 Properties of Kites and Trapezoids
Holt Geometry
6-6 Properties of Kites and Trapezoids
Example 6: Using Properties of Isosceles Trapezoids
Find mA.
Holt Geometry
6-6 Properties of Kites and Trapezoids
Example 7: Using Properties of Isosceles Trapezoids
KB = 21.9m and MF = 32.7.
Find FB.
Holt Geometry
6-6 Properties of Kites and Trapezoids
Example 8
Find mF.
Holt Geometry
6-6 Properties of Kites and Trapezoids
Example 9
JN = 10.6, and NL = 14.8.
Find KM.
Holt Geometry
6-6 Properties of Kites and Trapezoids
Example 10: Applying Conditions for Isosceles
Trapezoids
Find the value of a so that PQRS
is isosceles.
Holt Geometry
6-6 Properties of Kites and Trapezoids
Example 11: Applying Conditions for Isosceles
Trapezoids
AD = 12x – 11, and BC = 9x – 2. Find
the value of x so that ABCD is
isosceles.
Holt Geometry
6-6 Properties of Kites and Trapezoids
Example 12
Find the value of x so that
PQST is isosceles.
Holt Geometry
6-6 Properties of Kites and Trapezoids
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.
Holt Geometry
6-6 Properties of Kites and Trapezoids
Holt Geometry
6-6 Properties of Kites and Trapezoids
Example 13: Finding Lengths Using Midsegments
Find EF.
Holt Geometry
6-6 Properties of Kites and Trapezoids
Example 14
Find EH.
Holt Geometry
6-6 Properties of Kites and Trapezoids
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