Basic Mathematics for College Students

9.6 Quadrilaterals and Other Polygons 767

87. HEIGHT OF A TREE A tree casts a shadow of
    29 feet at the same time as a vertical yardstick casts a
    shadow of 2.5 feet. Find the height of the tree.


88. GEOGRAPHY The diagram below shows how a
    laser beam was pointed over the top of a pole to the
    top of a mountain to determine the elevation of the
    mountain. Find.

h

20 ft 6,000 ft

5 ft

9-ft

pole

Laser beam

h

2.5 ft 29 ft

3 ft

h

89. FLIGHT PATH An airplane ascends 200 feet as it
    flies a horizontal distance of 1,000 feet, as shown in
    the following figure. How much altitude is gained
    as it flies a horizontal distance of 1 mile?
    (Hint:1 mile 5,280 feet.)

WRITING

90. Tell whether the statement is true or false. Explain
    your answer.
    a. Congruent triangles are always similar.
    b. Similar triangles are always congruent.


91. Explain why there is no SSA property for congruent
    triangles.

REVIEW

Find the LCM of the given numbers.

92. 16, 20 93. 21, 27
    Find the GCF of the given numbers.


93. 18, 96 95. 63, 84

1 mi

x ft

200 ft

1,000 ft

SECTION 9.6

Quadrilaterals and Other Polygons

Recall from Section 9.3 that a polygon is a closed geometric figure with at least three
line segments for its sides. In this section, we will focus on polygons with four sides,
called quadrilaterals.One type of quadrilateral is the square.The game boards for
Monopoly and Scrabble have a square shape. Another type of quadrilateral is the
rectangle.Most picture frames and many mirrors are rectangular. Utility knife blades
and swimming fins have shapes that are examples of a third type of quadrilateral
called a trapezoid.

Objectives

1 Classify quadrilaterals.

2 Use properties of rectangles to

find unknown angle measures

and side lengths.

3 Find unknown angle measures

of trapezoids.

4 Use the formula for the sum of

the angle measures of a

polygon.

1 Classify quadrilaterals.

A quadrilateralis a polygon with four sides. Some common quadrilaterals are shown
below.

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) © iStockphoto.com/Tomasz Pietryszek