Parallel Lines

1
Parallel Lines Their Transversal

• What is a transversal?
• A line, ray, or segment that intersects two or
  more coplanar lines, rays or segments are
  different points.

2
Transversal

• Four lines are shown
• j, k, l, and m
• Which line is not a transversal?
• j is not a transversal of lines l and m. It
  intersects both line segments at the same point.
• k is a transversal of lines l and m
• l is a transversal of lines j and k
• m is a transversal of lines j and k

3
Pairs of angles formed by a transversal

• When a transversal intersect two lines it forms
  interior and exterior angles.
• The angles between the lines are interior.
• The angles above and below the lines are exterior

4
Exterior and Interior Angles

• Lines m and n are intersected by transversal t
• What angles are interior?
• lt2, lt3, lt 6, lt 7
• What angles are exterior?
• lt 1, lt4, lt5, lt 8

5
Corresponding Angles

• Angles formed by two lines and their transversal.
  One is interior, the other exterior and they are
  located on the same side of the transversal.

6
Corresponding Angles

• Identify the corresponding angles

• lt 1 corresponds to
• lt 3
• lt5 corresponds to
• lt7
• lt2 corresponds to
• lt 4
• lt 6 corresponds to
• lt 8

7

• If two lines cut by a transversal are parallel,
  then corresponding angles are congruent.
• Therefore
• lt 1
• lt 3
• lt 5 lt 7
• lt 2 lt 4
• lt 6 lt 8

8
Alternate Interior Angles

• Angles formed by a transversal that are located
  between the two lines and on opposite sides of
  the transversal

9
Alternate Interior Angles

• Identify the pairs of alternate interior angles.
• lt2 and lt 7
• lt6 and lt 3

10
Alternate Exterior Angles

• Angles formed by the transversal that are located
  outside of the lines and on opposite sides of the
  transversal.

11
Alternate Exterior Angles

• Identify the pairs of alternate exterior angles

• lt1 and lt 8
• lt 5 and lt 4

12
Same Side Interior Angles

• Angles located between the lines and on the same
  side of the transversal
• Identify the pairs of same-side interior angles
• lt 2 and lt 3
• lt 6 and lt 7

13
Same Side Exterior Angles

• Angles located outside the lines and on the same
  side of the transversal.
• lt 1 and lt 4
• lt 5 and lt 8

14
Angles formed by lines intersected by a
transversal

• Use the following diagram and identify each set
  of angles.
• Corresponding angles
• Alternate interior angles
• Alternate exterior angles
• Same-side interior angles
• Same-side exterior angles