trapezoids recognize and apply the properties of trapezoids. solve problems involving the medians...
DESCRIPTION
The base angles are formed by the base and one of the legs. The non-parallel sides are called legs. PROPERTIES OF TRAPEZOIDS JOHN B. CORLEY AB CD base leg A and B are base angles C and D are base anglesTRANSCRIPT
TRAPEZOIDS• Recognize and apply the properties oftrapezoids.• Solve problems involving the medians of
trapezoids.
Trapezoid building blocks
Text p. 439
JOHN B. CORLEY
A trapezoid is a quadrilateral with exactly one pair of parallel sides.
PROPERTIES OF TRAPEZOIDS
JOHN B. CORLEY
The base angles are formed by the base and one of the legs. The non-parallel sides are called legs.
PROPERTIES OF TRAPEZOIDS
JOHN B. CORLEY
A B
CD
base
base
legleg
A and B are base angles
C and D are base angles
If the legs are congruent, a trapezoid is an isosceles trapezoid.
PROPERTIES OF TRAPEZOIDS
JOHN B. CORLEY
A B
CD
If the legs are congruent, a trapezoid is an isosceles trapezoid.
PROPERTIES OF TRAPEZOIDS
JOHN B. CORLEY
Both pairs of base angles of an isosceles trapezoid are congruent
A B
CD
If the legs are congruent, a trapezoid is an isosceles trapezoid.
PROPERTIES OF TRAPEZOIDS
JOHN B. CORLEY
The diagonals of an isosceles trapezoid are congruent
A B
CD
Example 1 Identify Trapezoids
JKLM is a quadrilateral with vertices J(-18, -1), K(-6, 8), L(18, 1), and M(-18, -26).
10
8
6
4
2
-2
-4
-6
-8
-10
-12
-14
-16
-18
-20
-22
-24
-26
-25 -20 -15 -10 -5 5 10 15 20 25J
K
L
M
a. Verify that JKLM is a trapezoid
b. Determine whether JKLM is an isosceles trapezoid
(-18, -1)
(-6, 8)
(18, 1)
(-18, -26)
MEDIANS OF TRAPEZOIDS
median
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.
A B
CD
MEDIANS OF TRAPEZOIDS
A B
CD
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.
E FExample:EF = ½(AB + DC)
Example 2 Median of a Trapezoid
Q R
ST
X Y
QRST is an isosceles trapezoid with median XY
1 2
3 4
a. Find TS if QR = 22 and XY = 15
Example 2 Median of a Trapezoid
Q R
ST
X Y
QRST is an isosceles trapezoid with median XY
1 2
3 4
b. Find m1, m2, m3, and m4 if m1 = 4a – 10 and m3 = 3a + 32.5
Kites
A
B
C
D
A Kite is a quadrilateral with exactly two distinct pairs of adjacent congruent sides.
In kite ABCD, diagonal BD separates the kite into two congruent triangles. Diagonal AC separates the kite into two non-congruent isosceles triangles.