Download 9-2 Parallel and Perpendicular Lines Parallel lines are lines in a

9-2 Parallel and Perpendicular Lines
Parallel lines are lines in a plane that
never meet.
Perpendicular lines are lines that
intersect at 90° angles.
9-2 Parallel and Perpendicular Lines
The sides of the windows are transversals to the
top and bottom.
The top
and
bottom of
the
windows
are
parallel.
A transversal is a line that intersects two or more
lines that lie in the same plane. Transversals to
parallel lines form angles with special properties.
9-2 Parallel and Perpendicular Lines
Caution!
You cannot tell if angles are congruent by
measuring because measurement is not
exact.
9-2 Parallel and Perpendicular Lines
Additional Example 1: Identifying Congruent
Angles Formed by a Transversal
Measure the angles formed by the transversal
and parallel lines. Which angles seem to be
congruent?
9-2 Parallel and Perpendicular Lines
Additional Example 1 Continued
Angles circled in blue appear to be congruent to
each other, and angles circled in red appear to be
congruent to each other.
∠1 ≅ ∠3 ≅ ∠5 ≅ ∠7
∠2 ≅ ∠4 ≅ ∠6 ≅ ∠8
9-2 Parallel and Perpendicular Lines
Check It Out: Example 1
Measure the angles formed by the
transversal and the parallel lines. Which
angles appear to be congruent?
1
2
3 4
5 6
7 8
∠1, ∠4, ∠5, and ∠8 all measure 36° and appear
congruent.
∠ 2, ∠3, ∠6, and ∠7 all measure 144° and appear
congruent.
9-2 Parallel and Perpendicular Lines
Some pairs of the eight angles formed
by two parallel lines and a transversal
have special names.
9-2 Parallel and Perpendicular Lines
9-2 Parallel and Perpendicular Lines
Writing Math
The symbol for parallel is ||. The symbol
for perpendicular is ⊥.
9-2 Parallel and Perpendicular Lines
Additional Example 2B: Finding Angle Measures
of Parallel Lines Cut by Transversals Continued
In the figure, line l || line m. Find the
measure of the angle.
∠2
∠6
∠4
9-2 Parallel and Perpendicular Lines
Check It Out: Example 2A
In the figure, line n || line m. Find the
measure of each angle. Justify your
answer.
1 144°
m
∠5
3 4
5 6
n
7 8
∠7
∠8
∠6