Download properties of trapezoids

TRAPEZOIDS
Text p. 439
• Recognize and apply the properties of
trapezoids.
• Solve problems involving the medians of
trapezoids.
Trapezoid building
blocks
JOHN B. CORLEY
PROPERTIES OF TRAPEZOIDS
A trapezoid is a quadrilateral with exactly
one pair of parallel sides.
JOHN B. CORLEY
PROPERTIES OF TRAPEZOIDS
A and B are
base angles
A
base
B
leg
leg
D
base
C
C and D are base angles
The base angles are formed by the base
and one of the legs. The non-parallel sides
are called legs.
JOHN B. CORLEY
PROPERTIES OF TRAPEZOIDS
A
B
D
C
If the legs are congruent, a trapezoid is an
isosceles trapezoid.
JOHN B. CORLEY
PROPERTIES OF TRAPEZOIDS
A
B
Both pairs of base
angles of an
isosceles trapezoid
are congruent
D
C
If the legs are congruent, a trapezoid is an
isosceles trapezoid.
JOHN B. CORLEY
PROPERTIES OF TRAPEZOIDS
A
B
The diagonals of
an isosceles
trapezoid are
congruent
D
C
If the legs are congruent, a trapezoid is an
isosceles trapezoid.
JOHN B. CORLEY
Example 1
Identify Trapezoids
JKLM is a quadrilateral with vertices J(-18, -1),
K(-6, 8), L(18, 1), and M(-18, -26).
a. Verify that
JKLM is a
trapezoid
(-6, 8)
K
8
6
4
L
2
-25
J
-20
-15
-10
(-18, -1)
b. Determine
whether
JKLM is
an
isosceles
trapezoid
10
-5
-2
-4
-6
-8
-10
-12
-14
-16
-18
-20
-22
-24
M
(-18, -26)
-26
5
10
15
20
(18, 1)
25
MEDIANS OF TRAPEZOIDS
A
B
median
D
C
The segment that joins the midpoints of the legs
of a trapezoid is called the median.
The median of a trapezoid can also be called a
midsegment.
MEDIANS OF TRAPEZOIDS
A
Example:
EF = ½(AB + DC)
B
F
E
D
C
THEOREM
The median of a trapezoid is parallel to the
bases and its measure is one half the sum of
the measures of the bases.
Example 2
QRST is an
isosceles trapezoid
with median XY
Median of a Trapezoid
R
Q
1
2
Y
X
3
T
a. Find TS if QR = 22 and XY = 15
4
S
Example 2
QRST is an
isosceles trapezoid
with median XY
Median of a Trapezoid
R
Q
1
2
Y
X
3
T
4
S
b. Find m1, m2, m3, and m4 if m1 = 4a – 10
and m3 = 3a + 32.5
Kites
B
A
C
A Kite is a quadrilateral with
exactly two distinct pairs of
adjacent congruent sides.
D
In kite ABCD, diagonal BD separates the kite
into two congruent triangles. Diagonal AC
separates the kite into two non-congruent
isosceles triangles.