a trapezoid base legs base of a trapezoid are two consecutive … · 2018-07-05 · holt mcdougal...
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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
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 McDougal Geometry
6-6 Properties of Kites and Trapezoids
Holt McDougal Geometry
6-6 Properties of Kites and Trapezoids
Theorem 6-6-5 is a biconditional statement. So it is true both “forward” and “backward.”
Reading Math
Holt McDougal Geometry
6-6 Properties of Kites and Trapezoids
Isos. trap. s base
Example 3A: Using Properties of Isosceles
Trapezoids
Find mA.
Same-Side Int. s Thm.
Substitute 100 for mC.
Subtract 100 from both sides.
Def. of s
Substitute 80 for mB
mC + mB = 180°
100 + mB = 180
mB = 80°
A B
mA = mB
mA = 80°
Holt McDougal Geometry
6-6 Properties of Kites and Trapezoids
Example 3B: Using Properties of Isosceles
Trapezoids
KB = 21.9 and MF = 32.7.
Find FB.
Isos. trap. s base
Def. of segs.
Substitute 32.7 for FM.
Seg. Add. Post.
Substitute 21.9 for KB and 32.7 for KJ.
Subtract 21.9 from both sides.
KJ = FM
KJ = 32.7
KB + BJ = KJ
21.9 + BJ = 32.7
BJ = 10.8
Holt McDougal 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 McDougal 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 McDougal Geometry
6-6 Properties of Kites and Trapezoids
Example 4A: Applying Conditions for Isosceles
Trapezoids
Find the value of a so that PQRS is isosceles.
a = 9 or a = –9
Trap. with pair base s isosc. trap.
Def. of s
Substitute 2a2 – 54 for mS and a2 + 27 for mP.
Subtract a2 from both sides and add 54 to both sides.
Find the square root of both sides.
S P
mS = mP
2a2 – 54 = a2 + 27
a2 = 81
Holt McDougal 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 McDougal Geometry
6-6 Properties of Kites and Trapezoids
Check It Out! Example 4
Find the value of x so that PQST is isosceles.
Subtract 2x2 and add 13 to both sides.
x = 4 or x = –4 Divide by 2 and simplify.
Trap. with pair base s isosc. trap.
Q S
Def. of s
Substitute 2x2 + 19 for mQ and 4x2 – 13 for mS.
mQ = mS
2x2 + 19 = 4x2 – 13
32 = 2x2
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. In Lesson 5-1, you studied the Triangle Midsegment Theorem. The Trapezoid Midsegment Theorem is similar to it.
Holt McDougal Geometry
6-6 Properties of Kites and Trapezoids
Holt McDougal 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 McDougal 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. 8 = EH
1 16.5 = (25 + EH) 2
Holt McDougal 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°