Download Honors Geometry: Section 3.3 part 2 Parallel Lines

Geometry: Section 3.3
Properties of Parallel Lines
Two lines are parallel iff they are
coplanar and do not intersect.
To indicate that AB is parallel to CD
AB // CD
we write _______
Arrowheads are use to
indicate parallel lines
in a figure.
Noncoplanar lines which do not
intersect are called skew.
Recall that perpendicular lines are
two lines that intersect to form right angles.
Postulate 13: The Parallel Postulate
If there is a line and a point not on the line,
then there is exactly one line through the point
that will be parallel to the given line.
Postulate 14: The Perpendicular Postulate
If there is a line and a point not on the
line, then
there is exactly one line through the point that
will be perpendicular to the given line
Postulate 15
Corresponding Angles Postulate
(CAP)
If two parallel lines are cut by a
transversal, then corresponding
angles are congruent.
Theorem 3.4
Alternate Interior Angles Theorem
(AIAT)
If two parallel lines are cut by a
transversal, then alternate interior
angles are congruent.
Theorem 3.5
Same-Side Interior Angles Theorem
(SSIAT)
If two parallel lines are cut by a
transversal, then same-side interior
angles are supplementary.
Theorem 3.6
Alternate Exterior Angles Theorem
(AEAT)
If two parallel lines are cut by a
transversal, then alternate exterior
angles are congruent.
Examples: Find the value of the variable in each
problem.
3 x  5  7 x  11
16  4 x
4x
Examples: Find the value of the variable in each
problem.
3 y  5  7 y  11  180
10 y  6  180
10 y  186
y  18.6
Examples: Find the value of the variable in each
problem.
5w  8  3w  6  180
8w  14  180
8w  166
w  20.75
Theorem 3.7 Perpendicular
Transversal Theorem
If a transversal is perpendicular to
one of two parallel lines, then
the transversal is also perpendicular to the
second parallel line.