1. Angles and Parallel Lines
Lesson 3-2
Angles and Parallel Lines
Lesson 3-2: Angles and Parallel Lines

2. Lesson 3-2: Angles and Parallel Lines
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, eight angles of the following types are formed:
Exterior angles
Interior angles
Same Side (Consecutive) interior angles
Alternate exterior angles
Alternate interior angles
Corresponding angles t m n
Lesson 3-2: Angles and Parallel Lines

3. Vertical Angles & Linear Pair
Two angles that are opposite angles. Vertical angles are congruent.
 1   4,  2   3,  5   8,  6   7
Supplementary angles that form a line (sum = 180)
1 & 2 , 2 & 4 , 4 &3, 3 & 1,
5 & 6, 6 & 8, 8 & 7, 7 & 5 1 2 3 4 5 6 7 8
Lesson 3-2: Angles and Parallel Lines

4. 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 (Consecutive) interior angles
Same- Side (Consecutive) exterior angles
Continued…..
Lesson 3-2: Angles and Parallel Lines

5. Lesson 3-2: Angles and Parallel Lines
Corresponding Angles
Corresponding Angles: Two angles that occupy corresponding positions.
 2   6,  1   5,  3   7,  4   8 1 2 3 4 5 6 7 8
Lesson 3-2: Angles and Parallel Lines

6. Same Side (Consecutive) Angles
Same side (Consecutive) Interior Angles: Two angles that lie between parallel lines on the same sides of the transversal. Same Side (Consecutive) 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
Lesson 3-2: Angles and Parallel Lines

7. Lesson 3-2 : Angles and Parallel Lines
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
Lesson 3-2 : Angles and Parallel Lines

8. Lesson 3-2 : Angles and Parallel Lines
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°. t 16 15 14 13 12 11 10 9 8 7 6 5 3 4 2 1 s D C B A
Lesson 3-2 : Angles and Parallel Lines

9. Lesson 3-2 : Angles and Parallel Lines
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
Lesson 3-2 : Angles and Parallel Lines