Download Parallel and Perpendicular Lines

3-1 Parallel and
Perpendicular
Lines
3-1 Parallel Lines and
Transversals
• Identify the relationships between
two lines and planes.
• Parallel lines – Two or
more lines that are
coplanar and do not
intersect.
• Parallel planes – Two
or more planes that
do not intersect.
• Skew – Two lines that do not
intersect and are not coplanar.
Parallel Postulate
• If there is a line and a point not on
the line, then there is exactly one
line through the point parallel to the
given line.
Perpendicular Postulate
• If there is a line and a point not on
the line, then there is exactly one
line through the point perpendicular
to the give line.
Identifying Angles formed
by Transversals
• Transversal – A line that intersects
two or more coplanar lines at
different points.
t
• Interior angles
• <1, <2, <3, <4
• Exterior angles
• <5, <6, <7, <8
Corresponding Angles
• Angles on the same side of the
transversal.
• One angle is an interior angle and the
other is an exterior angle
• They are not adjacent
• <1 and <5
• <2 and <6
• <3 and <7
1 2
• <4 and <8
3 4
5
7 8
6
Alternate Interior Angles
• Two interior angles that lie between the
two lines on opposite sides of the
transversal.
• <4 and <5
• <3 and <6
1 2
3 4
5
7 8
6
Alternate Exterior Angles
• Two exterior angles that lie outside the
two lines on opposite sides of the
transversal.
• <1 and <8
• <2 and <7
1 2
3 4
5
7 8
6
Consecutive Interior Angles
• Two angles that lie between the two
lines on the same side of the
transversal.
• <3 and <5
• <4 and <6
1 2
3 4
5
7 8
6
• Consecutive interior angles are
sometimes called same side interior
angles.
• Name all planes parallel
ABC.
• Name all segments that
• Name all segments that
to HB.
• Name all segments that
FH.
• Name all segments
• Perpendicular to FC.
to plane
intersect AB
are parallel
are skew to
• Vertical angles
• Supplementary angles
• Exterior angles
• Interior angles
• Consecutive interior angles
• Alternate interior angles
• Alternate exterior angles
• Corresponding angles
t
m
1
2
4
3
6
8
5
7
l
Assignments
• Class work page 175 problems 1-20
• Homework page 176 problems 21-36