a kite is a quadrilateral with exactly two pairs of ... · holt geometry 6-6 properties of kites...
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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
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 Geometry
6-6 Properties of Kites and Trapezoids
Example 2A Continued
Substitute mCDF for mCBF.
Substitute 52 for mCBF.
Subtract 104 from both sides.
mBCD + mCBF + mCDF = 180°
mBCD + 52° + 52° = 180°
mBCD = 76°
mBCD + mCBF + mCDF = 180°
Holt 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 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 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
Theorem 6-6-5 is a biconditional statement. So it is true both “forward” and “backward.”
Holt Geometry
6-6 Properties of Kites and Trapezoids
Isos. trap. s base
Same-Side Int. s Thm.
Def. of s
Substitute 49 for mE.
mF + mE = 180°
E H
mE = mH
mF = 131°
mF + 49° = 180°
Simplify.
Check It Out! Example 3a
Find mF.
Holt Geometry
6-6 Properties of Kites and Trapezoids
Check It Out! Example 3b
JN = 10.6, and NL = 14.8. Find KM.
Def. of segs.
Segment Add Postulate
Substitute.
Substitute and simplify.
Isos. trap. s base
KM = JL
JL = JN + NL
KM = JN + NL
KM = 10.6 + 14.8 = 25.4
Holt Geometry
6-6 Properties of Kites and Trapezoids
Example 4B: Applying Conditions for Isosceles
Trapezoids
AD = 12x – 11, and BC = 9x – 2. Find the value of x so that ABCD is isosceles.
Diags. isosc. trap.
Def. of segs.
Substitute 12x – 11 for AD and 9x – 2 for BC.
Subtract 9x from both sides and add 11 to both sides.
Divide both sides by 3.
AD = BC
12x – 11 = 9x – 2
3x = 9
x = 3
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 5: Finding Lengths Using Midsegments
Find EF.
Trap. Midsegment Thm.
Substitute the given values.
Solve. EF = 10.75
Holt Geometry
6-6 Properties of Kites and Trapezoids
Check It Out! Example 5
Find EH.
Trap. Midsegment Thm.
Substitute the given values.
Simplify.
Multiply both sides by 2. 33 = 25 + EH
Subtract 25 from both sides. 13 = EH
1 16.5 = (25 + EH) 2
Holt Geometry
6-6 Properties of Kites and Trapezoids
Lesson Quiz: Part I
In kite HJKL, mKLP = 72°, and mHJP = 49.5°. Find each measure. 1. mLHJ 2. mPKL 81° 18°
Use the diagram for Items 4 and 5. 4. mWZY = 61°. Find mWXY. 6. Find LP.
119°
18