Basic Mathematics for College Students

768 Chapter 9 An Introduction to Geometry

A B

D C

A segment that joins two nonconsecutive vertices of a polygon is called a diagonal

of the polygon. Quadrilateral ABCDshown below has two diagonals,ACand BD.

The Language of Mathematics When naming a quadrilateral (or any other

polygon), we may begin with any vertex. Then we move around the figure in a

clockwise (or counterclockwise) direction as we list the remaining vertices.

Some other ways of naming the quadrilateral above are quadrilateral ,

quadrilateral ,and quadrilateral .It would be unacceptable to

name it as quadrilateral ,because the vertices would not be listed in

clockwise (or counterclockwise) order.

ACDB

CDAB DABC

ADCB

2 Use properties of rectangles to find unknown

angle measures and side lengths.

Recall that a rectangleis a quadrilateral with four right angles. The rectangle is

probably the most common and recognizable of all geometric figures. For example,

most doors and windows are rectangular in shape. The boundaries of soccer fields and

basketball courts are rectangles. Even our paper currency, such as the $1, $5, and $20

bills, is in the shape of a rectangle. Rectangles have several important characteristics.

Properties of Rectangles

In any rectangle:

1. All four angles are right angles.


2. Opposite sides are parallel.


3. Opposite sides have equal length.


4. The diagonals have equal length.


5. The diagonals intersect at their midpoints.

EXAMPLE (^1) In the figure, quadrilateral
is a rectangle. Find each measure:
a. b. c. d.
StrategyWe will use properties of rectangles to find the
unknown angle measure and the unknown measures of
the line segments.
WHYQuadrilateral WXYZis a rectangle.
m(YXW) m(XY) m(WY) m(XZ)
WXYZ 8 in.
6 in.
Y
Z
X
A
W
5 in.
We can use the capital letters that label the vertices
of a quadrilateral to name it. For example, when referring
to the quadrilateral shown on the right, with vertices ,
,,and , we can use the notation quadrilateral
ABCD.

B C D

A

A B

D C

Quadrilateral ABCD