Basic Mathematics for College Students

824 Chapter 9 An Introduction to Geometry

SECTION 9.6 Quadrilaterals and Other Polygons

A quadrilateralis a polygon with four sides. Use the

capital letters that label the vertices of a quadrilateral

to name it.

A segment that joins two nonconsecutive vertices of

a polygon is called a diagonalof the polygon.

DEFINITIONS AND CONCEPTS EXAMPLES

Quadrilateral WXYZ

X

W

Z

Y

Diagonal XZ

Diagonal WY

Rectangle ABCD

17 in. 16 in.

30 in. B

E

A

D C

Parallelogram

(Opposite sides

parallel)

Rectangle

(Parallelogram with

four right angles)

Square

(Rectangle with

sides of equal length)

Rhombus

(Parallelogram with

sides of equal length)

Trapezoid

(Exactly two

sides parallel)

Some special types of quadrilaterals are shown on the

right.

A rectangleis a quadrilateral with four right angles.

Properties of rectangles:

1.All four angles are right angles.

2.Opposite sides are parallel.

3.Opposite sides have equal length.

4.Diagonals have equal length.

5.The diagonals intersect at their midpoints.

1.

2. and


3. and


4. 
   

   5.m(DE)m(AE)m(EC)17 in.

   
   

m(DB)m(AC)34 in.

m(AD)16 in. m(DC)30 in.

ADBC ABDC

m(DAB)m(ABC)m(BCD)m(CDA)90°

Conditions that a parallelogram must meet to ensure

that it is a rectangle:

1.If a parallelogram has one right angle, then the

parallelogram is a rectangle.

2.If the diagonals of a parallelogram are congruent,

then the parallelogram is a rectangle.

Read Example 2 on page 769 to see how these two conditions are

used in construction to “square a foundation.”

12 ft

12 ft

9 ft

9 ft

AB

D C