learning objectives · learning objectives 7-5. holt geometry 6-6 properties of kites and...
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Holt Geometry
6-6 Properties of Kites and Trapezoids
To learn the properties of kites and trapezoids to solve problems.
Learning Objectives
7-5
Holt Geometry
6-6 Properties of Kites and Trapezoids
kite
trapezoid
base of a trapezoid
leg of a trapezoid
base angle of a trapezoid
isosceles trapezoid
midsegment of a trapezoid
Vocabulary
7-5
Holt Geometry
6-6 Properties of Kites and Trapezoids
A kite is a quadrilateral with exactly two pairs of congruent consecutive sides.
7-5
Holt Geometry
6-6 Properties of Kites and Trapezoids7-5
Holt Geometry
6-6 Properties of Kites and Trapezoids
Example 1: Using Properties of Kites
In kite ABCD, mDAB = 54°, and mCDF = 52°. Find mBCD.
7-5
Holt Geometry
6-6 Properties of Kites and Trapezoids
Example 2: Using Properties of Kites
In kite ABCD, mDAB = 54°, and mCDF = 52°. Find mABC.
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Holt Geometry
6-6 Properties of Kites and Trapezoids
Example 3: Using Properties of Kites
In kite ABCD, mDAB = 54°, and mCDF = 52°. Find mFDA.
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Holt Geometry
6-6 Properties of Kites and Trapezoids
In kite PQRS, mPQR = 78°, and mTRS = 59°. Find mQRT.
Example 4: Using Properties of Kites
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Holt Geometry
6-6 Properties of Kites and Trapezoids
In kite PQRS, mPQR = 78°, and mTRS = 59°. Find mQPS.
Example 5: Using Properties of Kites
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Holt Geometry
6-6 Properties of Kites and Trapezoids
In kite PQRS, mPQR = 78°, and mTRS = 59°. Find each mPSR.
Example 6: Using Properties of Kites
7-5
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.
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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.
7-5
Holt Geometry
6-6 Properties of Kites and Trapezoids7-5
Holt Geometry
6-6 Properties of Kites and Trapezoids
Example 7: Using Properties of Isosceles Trapezoids
Find mA.
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Holt Geometry
6-6 Properties of Kites and Trapezoids
Example 8: Using Properties of Isosceles Trapezoids
KB = 21.9m and MF = 32.7. Find FB.
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Holt Geometry
6-6 Properties of Kites and Trapezoids
Find mF.
Example 9: Using Properties of Isosceles Trapezoids
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Holt Geometry
6-6 Properties of Kites and Trapezoids
JN = 10.6, and NL = 14.8. Find KM.
Example 10: Using Properties of Isosceles
Trapezoids
7-5
Holt Geometry
6-6 Properties of Kites and Trapezoids
Example 11: Applying Conditions for Isosceles
Trapezoids
Find the value of a so that PQRSis isosceles.
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Holt Geometry
6-6 Properties of Kites and Trapezoids
Example 12: Applying Conditions for Isosceles
Trapezoids
AD = 12x – 11, and BC = 9x – 2. Find the value of x so that ABCD is isosceles.
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Holt Geometry
6-6 Properties of Kites and Trapezoids
Find the value of x so that PQST is isosceles.
Example 13: Applying Conditions for Isosceles
Trapezoids
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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.
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Holt Geometry
6-6 Properties of Kites and Trapezoids7-5
Holt Geometry
6-6 Properties of Kites and Trapezoids
Example 14: Finding Lengths Using Midsegments
Find EF.
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Holt Geometry
6-6 Properties of Kites and Trapezoids
Find EH.
Example 15: Finding Lengths Using Midsegments
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Holt Geometry
6-6 Properties of Kites and Trapezoids7-5
Practice Questions are in the workbook on Page 167:1,4,6,8,9,11,14
Practice Questions are in the workbook on Page 167:20,21,22,26,27,29
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