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Geometry
5.5
Trapezoids
Trapezoid (Defn.)
Memo about medians
A quadrilateral with exactly one pair of
parallel sides.
leg
The sides are
called the bases
The other sides
are called the legs
base
base
leg
IsoscelesTrapezoid (Defn.)
A trapezoid with congruent legs.
Theorem
Base angles of an isosceles trapezoid
are congruent.
Median of a Trapezoid
(Defn.)
A segment that joins the midpoints of the legs.
leg
median
leg
Theorem
The median of a trapezoid:
1. is parallel to the bases.
2. has a length equal to the average of the
base lengths.
A
XY = ½(AB + CD)
X
C
B
median
Y
D
1.
AB = 10
CD = 30
EF = x
A
E
C
2.
AB = x
CD = 18
EF = 12
B
F
D
A
E
C
B
F
D
3.
AB = x – 3
CD = 2x – 4
EF = 10
4.
AB = y – 4
CD = 7y + 6
EF = 5y – 3
A
E
C
B
A
F
E
D
C
B
F
D
5.
AB = 4x
CD = 10x
EF = x2 + 10
A
E
C
6.
AB = x
CD = 3x
EF = x2 - 48
B
A
F
E
D
C
B
F
D
7. One angle of an isosceles trapezoid
measures 68. Find the measures of the
other angles.
8. Two congruent angles of an isosceles
trapezoid have measures 2x+21 and
3x-15. Find the value of x and then
give the measures of all the angles.
Homework
pg. 192-193 CE 1-11 WE 1-18
Example
Find the length of the median of the trapezoid.
Median = ½(Base 1 + Base 2)
5x = ½ [(x + 12) + (7x – 2)]
5x = 25
x + 12
(2) 5x = 8x + 10
10x = 8x + 10
5x
2x = 10
x=5
7x -2
A few homework problems….
Let’s do P. 192-193 #8 and #15