1. 1.3b- Angles with parallel lines
CCSS
G-CO.9 Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints.

2. Transversal
A line that intersects 2 or more coplanar lines at different points.
transversal l m

3. Alternate Interior <s – Alternate Exterior <s - 2 l m
Interior <s -
Exterior <s -
Alternate Interior <s –
Alternate Exterior <s -
Consecutive Interior <s –
Corresponding <s -
<3, <4, <5, <6 (inside l & m)
<1, <2, <7, <8 (outside l & m)
<3 & <6, <4 & <5 (alternate –opposite sides of the transversal)
<1 & <8, <2 & <7
<3 & <5, <4 & <6
(consecutive – same side of transversal)
<1 & <5, <2 & <6, <3 & <7, <4 & <8 (same location)

5. Ex. n Name the following: Alt. Int- Alt ext- Corresponding-
Consecutive int-
Vertical- p m
2 &7 ;
5 &4
3 & 6 ;
1 & 8 1 2 3 5
1 & 5; 2 & 6 ; 4 & 8 ; 3 & 7 4 6
2 & 5 7 8
4 & 7
1 &4; 3 & 2; 5 & 8; 6 & 7

6. Identify any transversals

7. Corresponding s
If 2  lines are cut by a transversal, then the pairs of corresponding s are .
i.e. If l m, then 12. 1 2 l m

8. Alt. Int. s
If 2  lines are cut by a transversal, then the pairs of alternate interior s are .
i.e. If l m, then 12. 1 2 l m

9. Alt. Ext. ’s
If 2  lines are cut by a transversal, then the pairs of alternate exterior s are .
i.e. If l m, then 12.
l m 1 2

10. Consecutive Int. (same-side interior)
If 2  lines are cut by a transversal, then the pairs of consecutive int. s are supplementary.
i.e. If l m, then 1 & 2 are supp. l m 1 2

11. Consecutive Exterior. (same-side exterior)
If 2  lines are cut by a transversal, then the pairs of consecutive exterior. s are supplementary.
i.e. If l m, then 1 & 2 are supp. l m 1 2

13.  Transversal
If a transversal is  to one of 2  lines, then it is  to the other.
i.e. If l m, & t  l, then t m. t 1 2 l m

14. Ex: Find: m1= m2= m1=55o m2=125o m3= m3=55o m4= m4=125o m5=
x=40o 1
125o 2 3 5
x+15o

15. Ex.2. Solve for x and Find all the angle measures 8 4x-8 1 3 6x+ 12 9

17. Find m<1
Find m<1

25. The end 