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Holt McDougal Geometry
6-6 Properties of Kites and Trapezoids 6-6 Properties of Kites
and Trapezoids
Holt McDougal Geometry
Warm Up
Lesson Presentation
Lesson Quiz
Holt McDougal Geometry
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.
5 or –5
43
156
Holt McDougal Geometry
6-6 Properties of Kites and Trapezoids
Use properties of kites to solve problems.
Use properties of trapezoids to solve problems.
Objectives
Holt McDougal 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
Holt McDougal Geometry
6-6 Properties of Kites and Trapezoids
A kite is a quadrilateral with exactly two pairs of congruent consecutive sides.
Holt McDougal Geometry
6-6 Properties of Kites and Trapezoids
Holt McDougal Geometry
6-6 Properties of Kites and Trapezoids
Kite cons. sides
Example 2A: Using Properties of Kites
In kite ABCD, mDAB = 54°, and mCDF = 52°. Find mBCD.
∆BCD is isos. 2 sides isos. ∆
isos. ∆ base s
Def. of s
Polygon Sum Thm.
CBF CDF
mCBF = mCDF
mBCD + mCBF + mCDF = 180°
Holt McDougal Geometry
6-6 Properties of Kites and Trapezoids
Example 2A Continued
Substitute mCDF for mCBF.
Substitute 52 for mCDF.
Subtract 104 from both sides.
mBCD + mCDF + mCDF = 180°
mBCD + 52° + 52° = 180°
mBCD = 76°
mBCD + mCBF + mCDF = 180°
Holt McDougal Geometry
6-6 Properties of Kites and Trapezoids
Kite one pair opp. s
Example 2B: Using Properties of Kites
Def. of s
Polygon Sum Thm.
In kite ABCD, mDAB = 54°, and mCDF = 52°. Find mABC.
ADC ABC
mADC = mABC
mABC + mBCD + mADC + mDAB = 360°
mABC + mBCD + mABC + mDAB = 360°
Substitute mABC for mADC.
Holt McDougal Geometry
6-6 Properties of Kites and Trapezoids
Example 2B Continued
Substitute.
Simplify.
mABC + mBCD + mABC + mDAB = 360°
mABC + 76° + mABC + 54° = 360°
2mABC = 230°
mABC = 115° Solve.
Holt McDougal Geometry
6-6 Properties of Kites and Trapezoids
Kite one pair opp. s
Example 2C: Using Properties of Kites
Def. of s
Add. Post.
Substitute.
Solve.
In kite ABCD, mDAB = 54°, and mCDF = 52°. Find mFDA.
CDA ABC
mCDA = mABC
mCDF + mFDA = mABC
52° + mFDA = 115°
mFDA = 63°
Holt McDougal Geometry
6-6 Properties of Kites and Trapezoids
Check It Out! Example 2a
In kite PQRS, mPQR = 78°, and mTRS = 59°. Find mQRT.
Kite cons. sides
∆PQR is isos. 2 sides isos. ∆
isos. ∆ base s
Def. of s
RPQ PRQ
mQPT = mQRT
Holt McDougal Geometry
6-6 Properties of Kites and Trapezoids
Check It Out! Example 2a Continued
Polygon Sum Thm.
Substitute 78 for mPQR.
mPQR + mQRP + mQPR = 180°
78° + mQRT + mQPT = 180°
Substitute. 78° + mQRT + mQRT = 180°
78° + 2mQRT = 180°
2mQRT = 102°
mQRT = 51°
Substitute.
Subtract 78 from both sides.
Divide by 2.
Holt McDougal Geometry
6-6 Properties of Kites and Trapezoids
Check It Out! Example 2b
In kite PQRS, mPQR = 78°, and mTRS = 59°. Find mQPS.
Kite one pair opp. s
Add. Post.
Substitute.
Substitute.
QPS QRS
mQPS = mQRT + mTRS
mQPS = mQRT + 59°
mQPS = 51° + 59°
mQPS = 110°