trapezoids recognize and apply the properties of trapezoids. solve problems involving the medians...

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.