5-m inute c heck 1 1) lmno is a rhombus. find x. 2) lmno is a rhombus. find y. 3) qrst is a square....
TRANSCRIPT
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5-MINUTE CHECK 1
1) LMNO is a rhombus. Find x.
2) LMNO is a rhombus. Find y.
3) QRST is a square. Find n if mTQR = 8n + 8.
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6-6 TRAPEZOIDS AND KITES
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TRAPEZOID
Quadrilateral with one pair of parallel sides
Parallel sides are called the “bases”. Non-parallel sides are called the “legs”.
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ISOSCELES TRAPEZOID
Trapezoid where the legs are congruent
Diagonals are congruent.
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THEOREM
Base angles of an isosceles trapezoid are congruent.
What else can you tell me about angles x and y? They are supplements!
x x
y y
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TOO: FIND THE MISSING ANGLES
1)
2)
70 70
110 110
35 35
145 145
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THEOREM
The median of a trapezoid is parallel to the bases (Base + Base) divided by 2
b
b
m
2
b bm
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EXAMPLE: EF IS THE MEDIAN OF TRAPEZOID ABCD
1) If AB = 25 and DC = 13, find EF.2) If AB = 29 and EF = 24, find DC.
TOO: If AB = 7y + 6, EF = 5y – 3, and DC = y – 5, find y and EF. (both answers are decimals!!)
A
E
D C
F
B
25 13
2EF
19
2924
2
DC
19
3.5 14.5
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Kite
Is a Quadrilateral Diagonals are Perpendicular 2 consecutive sets of sides are congruent Longer diagonal bisects theAngles and the shorter diagonal.
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EXAMPLE If MNPQ is a kite, find NP.
NR2 + MR2 = MN2 Pythagorean Theorem(6)2 + (8)2 = MN2
36 + 64 = MN2
100 = MN2
10 = MN
Since MN NP, NP = 10.
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EXAMPLE
A. 28°
B. 36°
C. 42°
D. 55°
If BCDE is a kite, find mCDE.
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HOMEWORK
Pg. 444 #8-11, 16-27, 41-44