1. PARALLEL LINES, TRANSVERSALS
AND SPECIAL ANGLES
Section 3-1, 3-2
Jim Smith JCHS

2. A Line That Intersects 2 Or More Lines At Different Points Is
Called A Transversal
transversal

3. When This Happens, 8 Angles Are Formed1 2 3 4 5 6 7 8

4. This Forms 2 Neighborhoods1 2 3 4 5 6 7 8

5. Vertical And Linear Angles
Remember
Vertical And Linear Angles
Vertical 3 5 7 1 4 6 8 2

6. Linear Pairs 3 5 7 1 4 6 8 2

7. These Angles Are Called Consecutive Or Same Side Angles1 3 5 7 2 4 6 8

8. Interior Angles Exterior Angles (outside the lines) 5 3 4 6 1 7 2 8
(Between 2 lines)
Exterior Angles
(outside the lines) 1 2 7 8

9. Alternate Exterior Angles 1 And 8 Angles 2 And 7 Alternate Interior
Alternate Angles Are On
Different Sides Of The Transversal
And From Different Neighborhoods
Alternate Exterior
Angles 1 And 8
Angles 2 And 7
Alternate Interior
Angles 3 And 6
Angles 4 And 5 1 3 5 7 4 6 2 8

10. Consecutive Int
Angles 3 and 5
Angles 4 and 6 3 5 4 6
Consecutive Ext
Angles 1 and 7
Angles 2 and 8 1 7 8 2

11. Corresponding Angles Are 3 1 5 7 4 6 2 8
Corresponding Angles Are
Located In The Same Position In Each Neighborhood

12. Name The Angles 11 and 15 12 and 18 13 and 16 14 and 16 14 and 1817 18
11 and 15
12 and 18
13 and 16
14 and 16
14 and 18
11 and 14
15 and 17

13. Check Your Answers Corresponding Consecutive (Same Side) Interior
Alt Interior
Consecutive (SS) Exterior
Consecutive (SS) Interior
Vertical
Linear

14. Name the angles
1 and 3
7 and 12
11 and 14
6 and 10
13 and 5
9 and 6
1 and 13
5 an 4
7 and 11
6 and 11 4 3 2 1 8 7 6 5 12 11 9 10 16 15 14 13
With This Diagram, We Can Work With Angles In Different Neighborhoods As Long
As They Are Connected By A Transversal

15. Check Your Answers Corresponding Alt. Int. Cons. (SS) Int. Alt. Ext
None

16. Lines that are coplanar
Parallel lines
Lines that are coplanar
and do not intersect

17. If 2 Parallel Lines Are Cut By A Transversal Then:
Corresponding Angles
Are Congruent
Alternate Interior
Angles Are Congruent
Same Side Interior Angles
Are Supplementary

18. Even Without Parallel Lines Vertical Angles Are Always Congruent
Remember ………
Even Without Parallel Lines
Vertical Angles Are Always Congruent
Linear Pairs Are Always Supplementary

19. a b 1 2 3 4 5 6 7 8 a b
m 1 = 105
Find:
3 =
6 =
7 =
4 =
5 = 75
105

20. 119°
63° 1 2 a
61° 3 4
117°
119°
119°
63°
63° 5 6 b 7 8
119°

21. 2x+6 = 3x-10 5x-20+2x-10 = 180 6 = x – 10 7x-30 = 180 16 = x 7x = 210
a b
2x+6
4x+25
5x-20
6x-15
3x-10
2x-10
4x+25 = 6x-15
25 = 2x-15
40 = 2x
20 = x
2x+6 = 3x-10
6 = x – 10
16 = x
5x-20+2x-10 = 180
7x-30 = 180
7x = 210
x = 30