1. Angles and Parallel Lines
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Angles and Parallel Lines

2. Transversal
Definition: A line that intersects two or more lines in a plane at different points is called a transversal.
When a transversal t intersects line n and m, angles of the following types are formed:
Exterior angles
Interior angles
Same Side interior angles
Same side exterior angles
Alternative interior angles
Alternative exterior angles
Corresponding angles t m n

3. Alternate Angles
Alternate Interior Angles: Two angles that lie between parallel lines on opposite sides of the transversal (but not a linear pair).
Alternate Exterior Angles: Two angles that lie outside parallel lines on opposite sides of the transversal.
 3   6,  4   5
 2   7,  1   8 1 2 3 4 5 6 7 8

4. Same Side Angles (Consecutive Angles)
Same Side Interior Angles: Two angles that lie between parallel lines on the same sides of the transversal.
Same Side Exterior Angles: Two angles that lie outside parallel lines on the same sides of the transversal.
m3 +m5 = 180º, m4 +m6 = 180º 1 2
m1 +m7 = 180º, m2 +m8 = 180º 3 4 5 6 7 8

5. Corresponding Angles
Corresponding Angles: Two angles that occupy the same positions relative to the two lines.
 2   6,  1   5,  3   7,  4   8 1 2 3 4 5 6 7 8

6. Angles and Parallel Lines
If two parallel lines are cut by a transversal, then the following pairs of angles are congruent.
Corresponding angles
Alternate interior angles
Alternate exterior angles
If two parallel lines are cut by a transversal, then the following pairs of angles are supplementary.
Same side interior angles
Same side exterior angles
Continued…..

7. Example: If line AB is parallel to line CD and s is parallel to t, find the measure of all the angles when m  1 = 100°. Justify your answers. t 16 15 14 13 12 11 10 9 8 7 6 5 3 4 2 1 s D C B A
m  2=80° m  3=100° m  4=80°
m  5=100° m  6=80° m  7=100° m  8=80°
m  9=100° m  10=80° m  11=100° m  12=80°
m  13=100° m  14=80° m  15=100° m  16=80°

8. If line AB is parallel to line CD and s is parallel to t, find:
Example:
1. the value of x, if m  3 = 4x + 6 and the m  11 = 126.
2. the value of x, if m 1 = 100 and m 8 = 2x + 10.
3. the value of y, if m  11 = 3y – 5 and m  16 = 2y + 20. t 16 15 14 13 12 11 10 9 8 7 6 5 3 4 2 1 s D C B A
ANSWERS:
1. 30
2. 35
3. 33