Download 4.5 Parallel lines

Parallel Lines
Lesson 4.5
Objective:
Recognize planes and
transversals, identify the pairs of
angles formed by a transversal
and recognize parallel lines.
Plane:
•A surface with any two points
connected by a line. There must be
at least one point not on the line.
•Has only two dimensions, length
and width (infinite).
•Has no thickness.
y
x
Plane m
m
Coplanar:
• Points that lie on the same
plane (like collinear).
Non-coplanar:
• Points that do not lie on the
same plane.
Transversals:
• A line that intersects two
coplanar lines in two distinct
points. Not always parallel.
Parts of a transversal:
Exterior region
Interior region
Exterior region
Transversals angles:
• Alternate Interior Angles: angles on
opposite sides of the transversal in the
interior region.
• Alternate Exterior Angles: angles on
opposite sides if the transversal in the
exterior region.
• Corresponding Angles: angles in the same
position in relation to the transversal.
5
1
2
6
3
7
4
8
Name the alternate interior angles. 2 & 7
6 & 3
Name the alternate exterior angles.
1 & 8
5 & 4
Name the corresponding angles.
1 & 3, 2 & 4, 5 & 7, 6 & 8
Given: lines n and m are parallel cut
by transversal k
k
n
m
1
2
3
4
5
6
7
When the two lines cut by
the transversal are parallel,
certain angles are
congruent!
8
k
n
m
1
2
3
4
5
6
7
8
Alternate interior angles are congruent.
Alternate exterior angles are congruent.
Corresponding angles are congruent.
k
n
m
1
2
3
4
5
6
7
8
Name the alternate interior angles.
Name the alternate exterior angles.
Name the corresponding angles.
What other angles are congruent???
Notice: if you know one angle in a set of
transversal lines where two of the lines are
parallel, you know all eight angles.
Given: <1 = 45°name the other angles.
k
n
m
1
2
3
4
5
6
7
8
Parallel lines:
• Two coplanar lines that do not intersect.
(equidistance apart)
• Symbol ll or on lines > >
• Segments and rays can also be parallel.
• To be parallel, the lines MUST BE
COPLANAR!
Skew lines:
• Lines that never touch aren’t
coplanar or parallel!