8.5 Trapezoids and Kites
Trapezoid:
sides
a quadrilateral with exactly one pair of parallel
D
A
Bases : the pair of parallel sides in a trapezoid
Base angles: two pairs of angles in a trapezoid that lie on the
same base
Legs:
the nonparallel sides in a trapezoid
Isosceles trapezoid:
a trapezoid with congruent legs
Thm 8.14
If a trapezoid is isosceles, then each pair of base
angles is
B
A
D
C
C
B
Label: legs, bases, and each pair of base angles.
A
B
Legs:
Bases:
Base Angles:
How would this trapezoid be an isosceles trapezoid?
D
C
If a trapezoid has a pair of congruent base
angles, then it is an
E
Thm 8.15
F
H
Thm 8.16
A trapezoid is isosceles if and only
if its diagonals
K
Ex 1
CDEF is an isosceles trapezoid with CE = 10 and
m∠E = 95. Find DF, m∠C, m∠D, and m∠F.
D
E
F
Ex 2 Classify trapezoid QRST. Explain your reasoning.
If ST = 14 and m∠RST = 133º. Find QR and m∠Q.
R
S
Q
L
M
N
C
G
T
Ex 3 Show that XYZW is a
trapezoid.
X
4
2
Y
W
2
-2
4
6
-2
Z
midsegment (of a trapezoid):
the midpoints of its legs
the segment that connects
S
V
R
Q
Midsegment Theorem for Trapezoids
Thm 8.17
The midsegment of a trapezoid is
and its length is equal to
Pages 546 - 549 # 1, 2, 4-6, 8-12, 28, 38, 39, 44, 45
U
T
8.5 Trapezoids and Kites (day 2)
Ex 5 The vertices of a quatrilateral are K (-3,5), L (0,7),
M (2,7), and N (3, 5).
Is KLMN a trapezoid?
If it is, tell whether it is
isosceles and find the length
of its midsegment
Kite: a quadrilateral with two pairs of consecutive congruent
sides, but opposite sides are not congruent
T
R
O
P
B
If a quadrilateral is a kite,
Thm 8.18
then its diagonals
A
C
D
Thm 8.19
If a quadrilateral is a kite, then exactly one pair of
opposite angles are
A
D
B
C
W
Ex 6
WXYZ is a kite. Find RX
5
R
Z
X
Y
Ex 7
RSTU is a kite. m∠U = 125, m∠T = x, and
m∠R = x + 30. Find m∠T, m∠R, and m∠S.
1
Find the length of the midsegment RT
Ex 8
7
W
X
T
R
Y
Z
13
Ex 9
KITE is a kite. Find m∠K.
K
I
E 124o
32o
T
Ex 10
Find the side lengths of the kite. Write the lengths in
simplest radical form.
Q
5
P
8
5
R
5
S
Homework
Pages 546-549 # 14-17, 19-22, 25-27, 29, 34, 35, 47, 48