Download 6.6 Kites and Trapezoids

6-6 Properties of Kites and Trapezoids
Warm Up
Solve for x.
1. x2 + 38 = 3x2 – 12
2. 137 + x = 180
3.
4. Find FE.
Holt McDougal Geometry
6-6 Properties of Kites and Trapezoids
Holt McDougal Geometry
6-6 Properties of Kites and Trapezoids
• Kites and
trapezoids are
quadrilaterals
that do not fall
under the
category of
parallelograms.
Holt McDougal Geometry
6-6 Properties of Kites and Trapezoids
A kite is a quadrilateral with exactly two pairs of
congruent consecutive sides.
Kite Properties:
1. Diagonals are perpendicular.
2. Only the pair of non-vertex
angles are congruent.
3. Diagonals only bisect the
vertex angles.
4. Only the diagonal through
the non-vertex angles is
bisected.
Holt McDougal Geometry
6-6 Properties of Kites and Trapezoids
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 McDougal Geometry
6-6 Properties of Kites and Trapezoids
In kite ABCD, mDAB = 54°, and
mCDF = 52°.
1. Find mFDA.
2. Find mABC.
3. Find mBCD.
Holt McDougal Geometry
6-6 Properties of Kites and Trapezoids
In kite PQRS, mPQR = 78°,
and mTRS = 59°.
1. Find mQRT.
2. 2. Find mQPS.
3. Find mPSR.
Holt McDougal 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 McDougal Geometry
6-6 Properties of Kites and Trapezoids
Isosceles Trapezoid
•
•
•
•
•
•
The bases are parallel.
The legs are congruent.
Both pairs of base angles are congruent.
Leg angles add up to 180 degrees.
The diagonals are congruent.
Diagonals do not bisect each other.
Holt McDougal Geometry
6-6 Properties of Kites and Trapezoids
Find mA.
Holt McDougal Geometry
6-6 Properties of Kites and Trapezoids
KB = 21.9 and MF = 32.7.
Find FB.
Holt McDougal Geometry
6-6 Properties of Kites and Trapezoids
Find mF.
Holt McDougal Geometry
6-6 Properties of Kites and Trapezoids
JN = 10.6, and NL = 14.8.
Find KM.
Holt McDougal Geometry
6-6 Properties of Kites and Trapezoids
Find the value of a so that PQRS
is isosceles.
Holt McDougal Geometry
6-6 Properties of Kites and Trapezoids
AD = 12x – 11, and BC = 9x – 2. Find
the value of x so that ABCD is
isosceles.
Holt McDougal Geometry
6-6 Properties of Kites and Trapezoids
Find the value of x so that
PQST is isosceles.
Holt McDougal Geometry
6-6 Properties of Kites and Trapezoids
The midsegment of a trapezoid is the segment
whose endpoints are the midpoints of the legs.
Holt McDougal Geometry
6-6 Properties of Kites and Trapezoids
Find EF.
Holt McDougal Geometry
6-6 Properties of Kites and Trapezoids
Find EH.
Holt McDougal Geometry
6-6 Properties of Kites and Trapezoids
WXYZ is an isosceles trapezoid with bases WZ and XY
and median MN.
1. Find MN if WZ = 11 and XY =
3.
2. Find m∠ XMN if m∠WZN =
78.
Holt McDougal Geometry
6-6 Properties of Kites and Trapezoids
3. If MN = 10 and WZ = 14. Find
XY.
4. What is the value of x if
m∠MWZ = 15x – 5 and
m∠ WZN = 90 – 4x?
Holt McDougal Geometry
6-6 Properties of Kites and Trapezoids
5. If m∠XWZ = 2x – 7 and m∠XYZ
= 117. Find x.
6. If MN= 60, XY = 4x – 1, and WZ
= 6x + 11. Find x.
Holt McDougal Geometry
6-6 Properties of Kites and Trapezoids
7. If MN = 10x + 3, WZ = 11 and
XY = 8x + 19. Find x.
8. IF MN = 2x + 1, XY = 8 and
WZ = 3x – 3. Find x.
Holt McDougal 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?
In kite HJKL, mKLP = 72°,
and mHJP = 49.5°. Find each
measure.
2. mLHJ
Holt McDougal Geometry
3. mPKL
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.
5. XV = 4.6, and WY = 14.2. Find VZ.
6. Find LP.
Holt McDougal Geometry