Basic Mathematics for College Students

Chapter 9 Summary and Review 825

Trapezoid ABCD

A B

D C

Upper base

Lower base

Lower base

angles

Upper base

angles

Leg

Leg AB||DC

A trapezoidis a quadrilateral with exactly two sides
parallel.

The parallel sides of a trapezoid are called bases.The
nonparallel sides are called legs.

If the legs (the nonparallel sides) of a trapezoid are of
equal length, it is called an isosceles trapezoid.

In an isosceles trapezoid, both pairs of base angles
are congruent.

The sum S, in degrees, of the measures of the angles
of a polygon with sides is given by the formula

S(n2)180°

n

Find the sum of the angle measures of a hexagon.

Since a hexagon has 6 sides, we will substitute 6 for in the formula.

Substitute 6 for n,the number of sides.

Do the subtraction within the parentheses.

Do the multiplication.

The sum of the measures of the angles of a hexagon is 720°.

720°

(4)180°

S( 6 2)180°

S(n2)180°

n

We can use the formula to find the
number of sides a polygon has.

S(n2)180° The sum of the measures of the angles of a polygon is 2,340°. Find

the number of sides the polygon has.

Substitute 2,340° for S.

Now solve for n.

Distribute the multiplication by 180°.

Add 360° to both sides.

Do the addition.

Divide both sides by 180°.

Do the division.

The polygon has 15 sides.

15 n

2,700°

180 °



180°n

180 °

2,700°180°n

2,340° 360 °180°n360° 360 °

2,340°180°n360°

2,340°(n2)180°

S(n2)180°

59. Classify each of the following quadrilaterals as a
    parallelogram, a rectangle, a square, a rhombus, or a
    trapezoid. Some figures may be correctly classified
    in more than one way.
    a. b.

c. d.

e. f.

1 ft

2 ft

2 cm 2 cm

2 cm

2 cm

60. The length of diagonal of rectangle
    shown below is 15 centimeters. Find each measure.
    a.
    b.
    c.
    d.
    e.


61. Refer to rectangle below. Tell whether each
    statement is true or false.
    a.
    b.
    c. Triangle is isosceles.
    d.

WX

E

ZY

m(WY)m(WX)

WEX

m(ZE)m(EX)

m(WX)m(ZY)

WXYZ

m(AB)

m(EC)

m(2)

m(1)

m(BD)

AC ABCD

REVIEW EXERCISES

40°

50°

1

2

AB

E

DC14 cm