1. Parallel Lines & Transversals

2. Transversal
A line, ray, or segment that intersects 2 or more COPLANAR lines, rays, or segments.
transversal
transversal
Parallel lines
Non-Parallel lines

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

4. Special Angle Relationships
Interior Angles
∠3, ∠ 4, ∠ 5, ∠ 6
Alternate Interior Angles –
<3 & <6 are Alternate Interior angles
<4 & <5 are Alternate Interior angles 1 4 2 6 5 7 8 3

5. Special Angle Relationships
Interior Angles
∠ 3, ∠ 4, ∠ 5, ∠ 6
Alternate Interior Angles –
∠3 & ∠ 6 are Alternate Interior angles
∠ 4 & ∠ 5 are Alternate Interior angles 4 5 6 3 1 2 7 8

6. Special Angle Relationships
Interior Angles
∠ 3, ∠ 4, ∠ 5, ∠ 6
Alternate Interior Angles –
∠ 3 & ∠ 6 are Alternate Interior angles
∠ 4 & ∠ 5 are Alternate Interior angles 4 5 6 3 1 2 7 8

7. Special Angle Relationships
Same-Side Interior Angles –
∠ 3 & ∠ 5 are Same Side Interior angles
∠ 4 & ∠ 6 are Same Side Interior angles 5 6 4 1 2 7 8 3

8. Special Angle Relationships
Same-Side Interior Angles –
∠ 3 & ∠ 5 are Same Side Interior angles
∠ 4 & ∠ 6 are Same Side Interior angles 5 6 4 1 2 7 8 3

9. Special Angle Relationships1 4 2 6 5 7 8 3
Exterior Angles
∠1, ∠ 2, ∠ 7, ∠ 8

10. Special Angle Relationships7 8 1 4 2 6 5 3
Exterior Angles
∠ 1, ∠ 2, ∠ 7, ∠ 8

11. Special Angle Relationships1 4 2 6 5 7 8 3
Exterior Angles
∠ 1, ∠ 2, ∠ 7, ∠ 8
Alternate Exterior Angles –
∠2 & ∠ 7 are Alternate Exterior angles
∠ 1 & ∠ 8 are Alternate Exterior angles

12. Special Angle Relationships1 4 2 6 5 7 8 3
Exterior Angles
∠ 1, ∠ 2, ∠ 7, ∠ 8
Alternate Exterior Angles –
∠ 2 & ∠ 7 are Alternate Exterior angles
∠ 1 & ∠ 8 are Alternate Exterior angles

13. Special Angle Relationships1 4 2 6 5 7 8 3
Same-Side Exterior Angles –
∠ 1 & ∠ 7 are Same-Side Exterior angles
∠ 2 & ∠ 8 are Same-Side Exterior angles

14. Special Angle Relationships7 8 5 1 2 6 4 3
Same-Side Exterior Angles –
∠ 1 & ∠ 7 are Same-Side Exterior angles
∠ 2 & ∠ 8 are Same-Side Exterior angles

15. Special Angle Relationships1 4 2 6 5 7 8 3
Corresponding Angles: Angles that are in the same place
∠ 1 & ∠ 5 are Corresponding Angles
∠ 2 & ∠ 6 are Corresponding Angles
∠ 3 & ∠ 7 are Corresponding Angles
∠ 4 & ∠ 8 are Corresponding Angles

16. Special Angle Relationships1 4 2 6 5 7 8 3
Corresponding Angles: Angles that are in the same place
∠ 1 & ∠ 5 are Corresponding Angles
∠ 2 & ∠ 6 are Corresponding Angles
∠ 3 & ∠ 7 are Corresponding Angles
∠ 4 & ∠ 8 are Corresponding Angles

17. Special Angle Relationships1 4 2 6 5 7 8 3
Vertical Angles: Forms two touching “Vs” or looks like a bowtie
∠ 1 & ∠ 4 are Vertical Angles
∠ 2 & ∠ 3 are Vertical Angles
∠ 5 & ∠ 8 are Vertical Angles
∠ 6 & ∠ 7 are Vertical Angles

18. Special Angle Relationships1 4 2 6 5 7 8 3
Vertical Angles: Forms two touching “Vs” or looks like a bowtie
∠ 1 & ∠ 4 are Vertical Angles
∠ 2 & ∠ 3 are Vertical Angles
∠ 5 & ∠ 8 are Vertical Angles
∠ 6 & ∠ 7 are Vertical Angles

19. Special Angle Relationships1 4 2 6 5 7 8 3
Supplementary Angles: Add up to 180 degrees – form a straight line
Examples:
∠ 1 & ∠ 2 are Supplementary Angles
∠ 1 & ∠ 3 are Supplementary Angles
∠ 7 & ∠ 8 are Supplementary Angles
∠ 7 & ∠ 5 are Supplementary Angles

20. Parallel Lines & Transversals DAY #2

21. Special Angle Relationships WHEN THE LINES ARE PARALLEL
♥Alternate Interior Angles
are CONGRUENT
♥Alternate Exterior Angles are CONGRUENT 1 4 2 6 5 7 8 3
If the lines are not parallel, these angle relationships DO NOT EXIST.

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

23. Special Angle Relationships WHEN THE LINES ARE PARALLEL1 4 2 6 5 7 8 3
♥Corresponding Angles are CONGRUENT
♥Vertical Angles are
CONGRUENT
If the lines are not parallel, these angle relationships DO NOT EXIST.

24. Let’s Practice m<1=120° Find all the remaining angle measures. 1 46 5 7 8 3
120°
60°
m<1=120°
Find all the remaining angle measures.
120°
60°
120°
60°
120°
60°

25. Another practice problem
Find all the missing angle measures.
137°