1. Parallel Lines & Transversals & Angles

2. Transversal Definition:.
A line, ray, or segment that intersects 2 or more COPLANAR lines, rays, or segments.
transversal
transversal
Parallel lines
Non-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
Transversals, Angles and Parallel Lines

4. interior exterior INTERIOR –The space INSIDE the 2 lines
EXTERIOR The space OUTSIDE the 2 lines
exterior

5. Lesson 2-4: Angles and Parallel Lines

6. Transversals, Angles and Parallel Lines

7. Lesson 2-4: Angles and Parallel Lines
Transversal
When a transversal t intersects line n and m, eight angles of the following types are formed:
Exterior angles
Interior angles
Consecutive interior angles
Alternative exterior angles
Alternative interior angles
Corresponding angles t m n
Lesson 2-4: Angles and Parallel Lines

8. Special Angle Relationships
Interior Angles
<3 & <6 are Alternate Interior angles
<4 & <5 are Alternate Interior angles
<3 & <5 are Same Side Interior angles
<4 & <6 are Same Side Interior angles 1 4 2 6 5 7 8 3
Exterior Angles
<1 & <8 are Alternate Exterior angles
<2 & <7 are Alternate Exterior angles
<1 & <7 are Same Side Exterior angles
<2 & <8 are Same Side Exterior angles

9. Special Angle Relationships WHEN THE LINES ARE PARALLEL1 4 2 6 5 7 8 3
♥Alternate Interior Angles
are CONGRUENT
♥Alternate Exterior Angles are CONGRUENT
♥Same Side Interior Angles are SUPPLEMENTARY
♥Same Side Exterior Angles are SUPPLEMENTARY
If the lines are not parallel, these angle relationships DO NOT EXIST.

10. 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.
Consecutive interior angles
Consecutive exterior angles
Continued…..
Lesson 2-4: Angles and Parallel Lines

11. Corresponding Angles & Consecutive 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 2-4: Angles and Parallel Lines

12. Lesson 2-4: Angles and Parallel Lines
Consecutive Angles
Consecutive Interior Angles: Two angles that lie between parallel lines on the same sides of the transversal.
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 2-4: Angles and Parallel Lines

13. Lesson 2-4: 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 2-4: Angles and Parallel Lines

14. Lesson 2-4: 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°. 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°
Lesson 2-4: Angles and Parallel Lines

15. Lesson 2-4: 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 2-4: Angles and Parallel Lines

16. Let’s Practice 1 4 2 6 5 7 8 3 m<1=120°
Find all the remaining angle measures.
120°
60°
120°
60°
120°
60°
120°
60°

17. Another practice problem
40°
Find all the missing angle measures, and name the postulate or theorem that gives us permission to make our statements.
120°

18. Assignment
Section 3.1
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