Download GeomP5 4.1-4.2 - Parallel Lines, Planes, and Transversals.notebook

GeomP5 4.1­4.2 ­ Parallel Lines, Planes, and Transversals.notebook
October 14, 2016
Parallel Lines
Two lines are parallel iff they lie in the same plane and never intersect. l
m
l || m
Skew Lines
Two lines that are not in the same plane are skew lines iff they do not intersect. (Segments and rays that are part of skew lines are also skew). B
A
F
E
D
H
C
G
GeomP5 4.1­4.2 ­ Parallel Lines, Planes, and Transversals.notebook
October 14, 2016
Parallel Planes
Two planes are parallel planes iff they do not intersect.
B
A
F
E
D
C
H
G
Parallel Lines and Transversals
A transversal is a line that crosses two or more lines at different points. m
l
t
GeomP5 4.1­4.2 ­ Parallel Lines, Planes, and Transversals.notebook
October 14, 2016
Parallel Lines and Transversals
Interior Angles are the angles found between the two lines.
m
t
l
Parallel Lines and Transversals
Exterior Angles are the angles found outside the two lines.
m
l
t
GeomP5 4.1­4.2 ­ Parallel Lines, Planes, and Transversals.notebook
October 14, 2016
Parallel Lines and Transversals
Alternate Angles are two angles that are on different sides of the transversal.
m
t
l
Parallel Lines and Transversals
Consecutive Angles are two angles that are on the same side of the transversal.
m
l
t
GeomP5 4.1­4.2 ­ Parallel Lines, Planes, and Transversals.notebook
October 14, 2016
Parallel Lines, Transversals, and Angle Relationships
If a transversal crosses two parallel lines, then pairs of alternate interior angles are congruent.
Mark the diagram to reflect this statement. What conclusions can be made based on this statement?
t
1 2
l
3 4
5 6
m
7 8
Parallel Lines, Transversals, and Angle Relationships
If a transversal crosses two parallel lines, then pairs of alternate exterior angles are congruent.
Mark the diagram to reflect this statement. What conclusions can be made based on this statement?
t
1 2
l
3 4
5 6
7 8
m
GeomP5 4.1­4.2 ­ Parallel Lines, Planes, and Transversals.notebook
October 14, 2016
Parallel Lines, Transversals, and Angle Relationships
If a transversal crosses two parallel lines, then pairs of consecutive interior angles are supplementary.
Mark the diagram to reflect this statement. What conclusions can be made based on this statement?
t
1 2
l
3 4
5 6
m
7 8
Parallel Lines, Transversals, and Angle Relationships
Suppose the mL 2 = 110o. Find the measures of the other 7 angles.
t
1 2
l
3 4
5 6
7 8
m
GeomP5 4.1­4.2 ­ Parallel Lines, Planes, and Transversals.notebook
October 14, 2016
Parallel Lines, Transversals, and Angle Relationships
Suppose the mL 5 = 75o. Find the measures of the other 7 angles.
t
1 2
l
3 4
5 6
7 8
m