1. Insert Lesson Title Here
Properties of Parallel Lines
Insert Lesson Title Here
Vocabulary
Transversal
Supplementary Angles
Vertical Angles
Corresponding Angles
Alternate Interior Angles
Same Side Interior Angles

2. Parallel Lines
If two lines are intersected by a transversal and any of the angle pairs shown below are congruent, then the lines are parallel. This fact is used in the construction of parallel lines.

3. Properties of Parallel Lines
Angles marked in blue appear to be congruent to each other, and angles marked in red appear to be congruent to each other. 1 7 2 3 4 8 6 5 7 8

4. PROPERTIES OF TRANSVERSALS TO PARALLEL LINES
Properties of Parallel Lines
PROPERTIES OF TRANSVERSALS TO PARALLEL LINES
If two parallel lines are intersected by a transversal,
the acute angles that are formed are all congruent,
the obtuse angles are all congruent,
and any acute angle is supplementary to any obtuse angle.
If the transversal is perpendicular to the parallel lines, all of the angles formed are congruent 90° angles.

5. Example 1: Finding Angle Measures of Parallel Lines Cut by Transversals
In the figure, line l || line m. Find the measure of the angle. 4
All obtuse angles in the figure are congruent.
m4 = 124°

6. Example 2: Finding Angle Measures of Parallel Lines Cut by Transversals Continued
In the figure, line l || line m. Find the measure of the angle. 2
2 is supplementary to the angle 124°.
m ° = 180°
–124° –124°
m = 56°

7. Example 3: Finding Angle Measures of Parallel Lines Cut by Transversals Continued
In the figure, line l || line m. Find the measure of the angle. 6
All acute angles in the figure are congruent.
m6 = 56°
Course 3

8. Parallel Lines m7 = 144° Example 4
In the figure, line n || line m. Find the measure of the angle. 7
All obtuse angles in the figure are congruent
m7 = 144° 1
144° 3 4 5 6 7 8 m n

9. Example 5
In the figure, line n || line m. Find the measure of the angle. 5
5 is supplementary to the angle 144°. 1
144° 3 4 5 6 7 8 m n
m ° = 180°
–144° –144°
m = 36°

10. Example 6
In the figure, line n || line m. Find the measure of the angle. 1
All acute angles in the figure are congruent
m1 = 36° 1
144° 3 4 5 6 7 8 m n

11. In the figure a || b.
1. Name the angles congruent to 3.
1, 5, 7
2. Name all the angles supplementary to 6.
1, 3, 5, 7
3. If m1 = 105° what is m3?
105°
4. If m5 = 120° what is m2?
60°