1. 3.1 Parallel Lines, Transversals and Angle Relationships
Obj: 1.) to ID relationships of 2 planes and 2 lines
2.) to name angles formed by 2 lines and transversals

2. Definition
Skew lines - 2 lines are skew if they do NOT intersect and are NOT in the same plane
Draw and label this box in your notes. D F G A H B C E
Label all segments skew to AB
CE, DF, FG, EH

3. Definitions Continued
Parallel lines-2 Lines that are in the same plane that never intersect.
Transversal-Line that intersects 2 lines at different points. It’s the line in both angles when describing angle relationships.

4. Exterior angles 1 2 4 3 5 6 8 7
transversal l m t
Outside the 2 lines

5. Interior Angles 1 2 4 3 5 6 8 7
transversal l m t
Inside the 2 lines

6. *Consecutive-interior Angles…aka co-interior Angles1 2 4 3 5 6 8 7
transversal l m t
Angles inside the 2 lines on the same side of the transversal

7. *Alternate Interior Angles1 2 4 3 5 6 8 7
transversal l m t
Angles on the inside of the 2 lines and on opposite sides of the transversal

8. *Corresponding Angles1 2 4 3 5 6 8 7
transversal l m t
Angles in the same spot. Both above the lines on the same side of the transversal or below lines on same side of the transversal

9. *Alternate Exterior Angles1 2 4 3 5 6 8 7
transversal l m t
Outside the 2 lines on opposite sides of the transversal

10. Angle Relationship Definitions
Exterior angles- outside 2 lines
Alternate interior angle- opposite sides of transversal inside the 2 lines
Angles 1, 2, 7, 8
Angles 3 & 5, 4 & 6
Interior angles- inside the 2 lines
Alternate exterior angle-opposite sides of transversal, outside the lines
Angles 3, 4, 5, 6
Co-interior angles- same side of transversal inside the 2 lines
Angles 2 & 8, 1 & 7
Angles 4 & 5, 3 & 6

11. Angle Relationship Definitions Continued
Corresponding angles- same side of transversal in same position
Angles 1 & 5, 4 & 8, 2 & 6, 3 & 7

12. Example: 7 4 5 11 3 9 12 6 10 2 8 1 t l m ID each pair of angles
A.E.A
Co-int < s
Angles 9 & 11
Angles 7 & 12
A.I.A
A.I.A
Angles 4 & 8
Angles 1 & 5
Corr. < s
Corr. < s

13. Your Turn: 3 2 7 8 10 12 5 4 11 9 6 1 m t l ID transversal to l & m
Line t or t
ID the relationship between the following angles.
7 & 12
2 & 12
8 & 10
Corr < s
A.I.A
A.E.A

14. What’s the angle relationship of angles 1 and 2?
The lines are parallel
What do the arrows mean? 2
Corresponding: Notice they are in the same position so
they are congruent.

15. What’s the angle relationship of angles 1 and 2?
Alternate Exterior Angles: Notice they are vertical so they
are congruent.

16. What’s the angle relationship of angles 1 and 2?
Alternate Interior Angles: Notice they are vertical so they
are congruent.

17. What’s the angle relationship of angles 1 and 2?
Consecutive Interior Angles: Notice they supplementary.
Watch

18. So if lines are parallel, we know?
If 2 ll lines are cut by a transversal, then each pair of corresponding angles is congruent (postulate that can be used in all proofs)
If 2 ll lines are cut by a transversal, then each pair of alternate interior angles is congruent
If 2 ll lines are cut by a transversal, then each pair of consecutive interior angles is supplementary
If 2 ll lines are cut by a transversal, then each pair of alternate exterior angles are congruent

19. Perpendicular Transversal Theorem
In a plane, if a line is perpendicular to 1 of 2 ll lines, then it is perpendicular to the other.

20. Example: Given p ll q, l is transversal of p and q Prove: Statement1 2 p 3 4 5 6 q
Prove: 7 8
Statement
Justification
1.) p II q
1.) given
2.) Corr < s
3.) vert. < s
4.) Substitution

21. Example:
In the figure, l II m and c ll d. Find the values of x, y, and z. c d m l
14zo
(2x + 5)o
98o
(3y + 8)o
14z = 98 (AIA)
z = 7
98 + 2x + 5 = 180 (co-int)
x = 38.5
3y + 8 = 98 (AEA)
y = 30

22. Homework: Put this in your agenda pg 150 18 – 27