Page 704 - Basic College Mathematics with Early Integers

CHAPTER HIGHLIGHTS 681

Definitions and Concepts Examples

Section 9.1 Lines and Angles (continued)

When two lines intersect, four angles are formed. Two of
a
these angles that are opposite each other are called d c b
vertical angles. Vertical angles have the same measure.
Two of these angles that share a common side are called Vertical angles: Adjacent angles:
adjacent angles. Adjacent angles formed by intersecting ∠a and ∠c ∠a and ∠b
lines are supplementary. ∠d and ∠b ∠b and ∠c
A line that intersects two or more lines at different points ∠c and ∠d
is called a transversal. Line l is a transversal that inter- ∠d and ∠a
sects lines m and n. The eight angles formed have special
names. Some of these names are:
Corresponding angles: ∠a and ∠e, ∠c and ∠g, ∠b and
∠f, ∠d and ∠h
Alternate interior angles: ∠c and ∠f, ∠d and ∠e
ab m
PARALLEL LINES CUT BY A TRANSVERSAL cd
If two parallel lines are cut by a transversal, then the mea- ef n
sures of corresponding angles are equal and the measures gh
of alternate interior angles are equal.
l
Section 9.2 Plane Figures and Solids

The sum of the measures of the angles of a triangle is 180°. Find the measure of ∠x.

85
x 45

The measure of ∠x = 180° - 85° - 45° = 50°
A right triangle is a triangle with a right angle. The side
opposite the right angle is called the hypotenuse, and hypotenuse
leg
the other two sides are called legs.
leg

For a circle or a sphere: Find the diameter of the circle.
diameter = 2 # radius
6 ft
R T b
#
d = 2 r
diameter #
radius = d = 2 r
2
#
= 2 6 feet = 12 feet
∂ ∂
d
r =
2