8.6 Trapezoids and Kites.notebook
March 23, 2017
Trapezoid Definitions
A trapezoid is a quadrilateral with exactly one pair of parallel sides.
base angles 1
base angles 1
The parallel sides are called bases.
base 1
Trapezoids and Kites
leg
leg
base 2
The non­parallel sides are called legs.
base angles 2
base angles 2
The angles at the end of each base are called base angles. There are two pairs of base angles, one at each of the two bases. Feb 12­9:40 AM
Feb 12­9:46 AM
Trapezoid Facts
1. A trapezoid with congruent legs is called isosceles.
2. If a trapezoid is isosceles, then each pair of base angles are congruent. 3. If a trapezoid is isosceles, then the consecutive base angles are supplementary. x
x
y
y
x + y = 180
Solve for x:
Solve for x and y:
5x­5
x
ο
C
B
AC = 27
55
BD = 3y + 9
ο
A
20
D
4. A trapezoid is isosceles if and only if its diagonals are congruent.
Feb 12­9:55 AM
Feb 12­10:05 AM
1
8.6 Trapezoids and Kites.notebook
Trapezoid Midsegments
March 23, 2017
Solve for x:
The midsegment of a trapezoid is parallel to the bases and half the length of the sum of the two bases. 24
37
59
7x
base 1
midsegment
x
32
mid = 1/2 (base 1 + base 2)
base 2
Feb 12­10:44 AM
Feb 12­10:51 AM
Kite Definition and Facts
Find <I and <K
1. A kite is a quadrilateral that has two pairs of consecutive sides congruent, but opposite sides are NOT congruent.
<E = 124
ο
<T = 32
Find <T and solve for x.
ο
<E = 3x­3
<K = 73
ο
<I = 132
K
ο
K
I
E
I
E
2. If a quadrilateral is a kite, then its diagonals are perpendicular.
T
T
3. If a quadrilateral is a kite, then exactly one pair of opposite angles are congruent.
Feb 12­10:56 AM
Feb 12­11:05 AM
2