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
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.
6-6 TRAPEZOIDS AND KITES
TRAPEZOID
Quadrilateral with one pair of parallel sides
Parallel sides are called the “bases”. Non-parallel sides are called the “legs”.
ISOSCELES TRAPEZOID
Trapezoid where the legs are congruent
Diagonals are congruent.
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
TOO: FIND THE MISSING ANGLES
1)
2)
70 70
110 110
35 35
145 145
THEOREM
The median of a trapezoid is parallel to the bases (Base + Base) divided by 2
b
b
m
2
b bm
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
Kite
Is a Quadrilateral Diagonals are Perpendicular 2 consecutive sets of sides are congruent Longer diagonal bisects theAngles and the shorter diagonal.
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.
EXAMPLE
A. 28°
B. 36°
C. 42°
D. 55°
If BCDE is a kite, find mCDE.
HOMEWORK
Pg. 444 #8-11, 16-27, 41-44