Basic Mathematics for College Students

Chapter 9 Summary and Review 815

SECTION 9.2 Parallel and Perpendicular Lines

If two lines lie in the same plane, they are called coplanar.

Parallel linesare coplanar lines that do not intersect.

We read the symbol as “is parallel to.”

Perpendicular linesare lines that intersect and form right

angles.

We read the symbol as “is perpendicular to.”⊥



DEFINITIONS AND CONCEPTS EXAMPLES

Parallel lines Perpendicular lines

A line that intersects two coplanar lines in two distinct

(different) points is called a transversal.

When a transversal intersects two coplanar lines, four

pairs of corresponding anglesare formed.

If two parallel lines are cut by a transversal,corresponding

angles are congruent(have equal measures).

When a transversal intersects two coplanar lines, two

pairs of interior anglesand two pairs of alternate interior

anglesare formed.

If two parallel lines are cut by a transversal,alternate

interior angles are congruent(have equal measures).

If two parallel lines are cut by a transversal,interior angles

on the same side of the transversal are supplementary.

Transversal

l 1

l 2

l 1 l 2

1 2

3 4

5 6

7 8

Corresponding angles

•  1   5


•  2   6


•  3   7


•  4   8

Transversal

l 1

l 2

l 1 l 2

1 2

3 4

Alternate interior angles

•  1   4


•  2   3
  Interior angles
  m(1)  m( 3 ) = 180°
  m( 2 )  m(4) = 180°

We can use algebra to find the unknown measures of

corresponding angles.

In the figure,. Find x

and the measure of each

angle that is labeled.

Since the lines are parallel,

and the angles are

corresponding angles, the

angles are congruent.

The angle measures are equal.

Subtract 4xfrom both sides.

To isolate x,subtract 15° from both sides.

Thus,xis 20°. To find the measures of the angles labeled in

the figure, we evaluate each expression for.

The measure of each angle is 115°.

115° 115°

100°15° 80°35°

5 x15°5(20°)15° 4 x35°4(20°)35°

x20°

x20°

x15°35°

5 x15° 4 x35°

l 1 l 2

l 1

l 2

5 x + 15°

4 x + 35°