Parallel Lines Lesson 4.5

1
Parallel LinesLesson 4.5
2

• Objective
• Recognize planes and transversals, identify the
  pairs of angles formed by a transversal and
  recognize parallel lines.

3

• 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
m
Plane m
4

• Coplanar
• Points that lie on the same plane (like
  collinear).

• Non-coplanar
• Points that do not lie on the same plane.

5

• 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

6

• Transversals angles
• Alternate Interior Angles angles on opposite
  sides of the transversal in the interior region.
• Alternate Exterior Angles angles on opposite
  sides of the transversal in the exterior region.
• Corresponding Angles angles in the same
  position in relation to the transversal.

7
5
1
6
2
3
7
4
8
?2 ?7 ?6 ?3
Name the alternate interior angles. Name the
alternate exterior angles. Name the
corresponding angles.
?1 ?8 ?5 ?4
?1 ?3, ?2 ?4, ?5 ?7, ?6 ?8
8
Given lines n and m are parallel cut by
transversal k
7
When the two lines cut by the transversal are
parallel, certain angles are congruent!
9
7
Alternate interior angles are congruent. Alternate
exterior angles are congruent. Corresponding
angles are congruent.
10
7
Name the alternate interior angles. Name the
alternate exterior angles. Name the corresponding
angles. What other angles are congruent???
11
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 lt1
45name the other angles.
7
12

• Parallel lines
• Two coplanar lines that do not intersect.
  (equidistance apart)
• Symbol ll or on lines gt gt
• Segments and rays can also be parallel.
• To be parallel, the lines MUST BE COPLANAR!

13

• Skew lines
• Lines that never touch arent coplanar or
  parallel!