726 Chapter 9 An Introduction to Geometry
(a) (b)l 1 l 2 l 1 l 2Parallel lines Perpendicular linesParallel LinesParallel lines are coplanar lines that do not intersect.The Language of Mathematics If lines (read as “lsub 1”) and
(read as “lsub 2”) are parallel, we can write , where the symbol is read
as “is parallel to.”If lines and are perpendicular, we can write , where the symbol is
read as “is perpendicular to.”l 1 l 2 l 1 ⊥ l 2 ⊥l 1 l 2 l 1 l 2Perpendicular LinesPerpendicular lines are lines that intersect and form right angles.2 Identify corresponding angles, interior angles,
and alternate interior angles.
A line that intersects two coplanar lines in two distinct
(different) points is called a transversal.For example,
line in the figure to the right is a transversal
intersecting lines and.
When two lines are cut by a transversal, all eight
angles that are formed are important in the study of parallel lines. Descriptive names
are given to several pairs of these angles.
In the figure below, four pairs of corresponding anglesare formed.Corresponding angles- and
- and
- and
- 4 and 8
2 6
3 7
1 5
l 2 l 3l 1l 1l 2l 3Transversall 3l 1l 2 1 23 45 67 8TransversalCorresponding AnglesIf two lines are cut by a transversal, then the angles on the same side of the
transversal and in corresponding positions with respect to the lines are called
corresponding angles.Some lines that intersect are perpendicular. See figure (b) above.