holt geometry 6-6 properties of kites and trapezoids 6-6 properties of kites and trapezoids holt...
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Holt Geometry
6-6 Properties of Kites and Trapezoids6-6 Properties of Kites and Trapezoids
Holt Geometry
Warm UpWarm Up
Lesson PresentationLesson Presentation
Lesson QuizLesson Quiz
Holt Geometry
6-6 Properties of Kites and Trapezoids
Do NowSolve for x.
1. x2 + 38 = 3x2 – 12
2. 137 + x = 180
3.
4. Find FE.
Holt Geometry
6-6 Properties of Kites and Trapezoids
TSW use properties of kites and trapezoids to solve problems.
Objectives
Holt Geometry
6-6 Properties of Kites and Trapezoids
kitetrapezoidbase of a trapezoidleg of a trapezoidbase angle of a trapezoidisosceles trapezoidmidsegment of a trapezoid
Vocabulary
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, mDAB = 54°, and mCDF = 52°. Find mBCD.
Holt Geometry
6-6 Properties of Kites and Trapezoids
Example 3.5: Using Properties of Kites
In kite ABCD, mDAB = 54°, and mCDF = 52°. Find mABC.
Holt Geometry
6-6 Properties of Kites and Trapezoids
Example 4: Using Properties of Kites
In kite ABCD, mDAB = 54°, and mCDF = 52°. Find mFDA.
Holt Geometry
6-6 Properties of Kites and Trapezoids
Example 5
In kite PQRS, mPQR = 78°, and mTRS = 59°. Find mQRT.
Holt Geometry
6-6 Properties of Kites and Trapezoids
Example 5a
In kite PQRS, mPQR = 78°, and mTRS = 59°. Find mQPS.
Holt Geometry
6-6 Properties of Kites and Trapezoids
Example 5b
In kite PQRS, mPQR = 78°, and mTRS = 59°. Find each mPSR.
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 mA.
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 mF.
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?
In kite HJKL, mKLP = 72°,and mHJP = 49.5°. Find eachmeasure.
2. mLHJ 3. mPKL
about 191.2 in.
81° 18°
Holt Geometry
6-6 Properties of Kites and Trapezoids
Lesson Quiz: Part II
Use the diagram for Items 4 and 5.
4. mWZY = 61°. Find mWXY.
5. XV = 4.6, and WY = 14.2. Find VZ.
6. Find LP.
119°
9.6
18