This document discusses parallel lines cut by a transversal and the angle relationships that are formed. It defines key terms like transversal, interior angles, exterior angles, corresponding angles, same-side interior angles, alternate interior angles, same-side exterior angles, and alternate exterior angles. The main points are that when parallel lines are cut by a transversal, alternate interior angles are congruent, alternate exterior angles are congruent, same-side interior angles are supplementary, and same-side exterior angles are supplementary. Examples are provided to illustrate these relationships.

1. Parallel Lines Cut By A Transversal

2. STUDENT LEARNING OBJECTIVES​:
- Students will be able to define & identify transversal lines and the segment that they
intersect.
- Students will be able to identify the different types of angles formed at the
intersections of the transversal lines.
- Students will be able to define the special relationships of angles that are formed when
parallel lines are cut by a transversal:
Vertical Angles, Linear Pair of Angles, Same-Side Interior Angles, Same-Side Exterior
Angles, Alternate Interior Angles, and Alternate Exterior Angles.

3. Vertical Angles
Opposite angles formed by intersecting lines.
Vertical angles are always equal (parallel or not parallel).

4. Linear Pair of Angles
Adjacent Angles or “side by side” angles creating a straight line.
If two angles form a linear pair, they are supplementary.

5. Parallel Lines and Transversals
Today we will learn to identify the relationships among
interior and exterior angles formed by two parallel lines
and a transversal.

6. Parallel Lines and Transversals
A line, line segment, or ray that intersects two or more lines at
different places is called a __________TRANSVERSAL
M
J
B
A
AB is an example of a transversal.
It intercepts lines M and J.
View the angles formed between the intersections.
1 2
34
5
7
6
8

7. Parallel Lines and Transversals
Transversal A line that intersects two or more lines, each at different points.
The lines cut by a transversal may or may not be Parallel.
l
m
1 2
34
5
7
6
8
ml
Parallel Lines
T is a transversal for l and m.
T
1 2
34
5
7
6
8
O
P
PO ||
Nonparallel Lines
V is a transversal for O and P.
V

8. Parallel Lines and Transversals
Two lines divide the plane into three regions.
The region “inside” the lines is called the interior.
The two regions “outside” the lines is called the exterior.
Exterior
Exterior
INTERIOR

9. l
m
1 2
34
5
7
6
8
Parallel Lines and Transversals
When a transversal intersects two lines, _____ angles are formed.EIGHT
t
Interior angles are “inside” the
two lines (L) & (M).
Exterior angles are “outside” the
two lines (L) & (M).
Alternate Interior angles are on the
opposite sides of the transversal &
“inside” the lines.
Same Side Interior angles are on
the same side of the transversal &
“inside” the lines.
Alternate Exterior angles are
on the opposite sides of the
Transversal & “outside” the lines.
Same Side Exterior angles are on
the same side of the transversal &
“outside” the lines.
Alternate angles lie on OPPOSITE
sides of the transversal (T).
Same Side angles lie on the SAME
side of the transversal (T).

10. Corresponding Angles
Corresponding
Angles
Corresponding Angles are in the same position at each
intersection.
Corresponding Angles is _________.
1 2
34
5
7
6
8
73  51 
congruent

11. Same Side Interior Angles
1 2
34
5
7
6
8
Same Side
Interior
Angles
Same Side Interior Angles are between the intersected lines &
on the same side of the transversal.
The pair of Same Side Interior angles is _____________.supplementary
18054  18063 

12. Alternate Interior Angles
Alternate
Interior
Angles
Alternate Interior Angles are between the intersected lines and on
opposite sides of the transversal
Each pair of Alternate interior angles is _________.
1 2
34
5
7
6
8
64  53 
congruent

13. Same Side
Exterior
Angles
If two parallel lines are cut by a transversal, then each pair of
Same side exterior angles is _____________.
Same Side Exterior Angles
1 2
34
5
7
6
8
supplementary
18081  18072 

14. Alternate Exterior Angles
1 2
34
5
7
6
8
Alternate
Exterior
Angles
If two parallel lines are cut by a transversal, then each pair of
alternate exterior angles is _________.congruent
71  82 

15. Angle Pair Relationships
Concept
Summary
Congruent Supplementary
alternate interior angles
alternate exterior angles
same side interior angles
Angle pairs formed when
a transversal cuts two parallel lines.
vertical angles linear pair of angles
same side exterior angles

16. m<1=120°
Find all remaining angles.
1
4
2
65
7 8
3
60°
60°
60°
60°
120°
120°
120°
120°
LET’S PRACTICE!

17. Another practice problem
Find all the
missing angle
measures, and
explain how you
found them!
40°
120°
120°
60°
60°
40°
60°
60°
180-(40+60)= 80°
80°
80°
80°
100°
100°
MORE PRACTICE!

18. SUMMARY: WHEN THE LINES ARE PARALLEL
1) Alternate Interior Angles
are CONGRUENT
2) Alternate Exterior Angles
are CONGRUENT
3) Same Side Interior Angles
are SUPPLEMENTARY
4) Same Side Exterior Angles
are SUPPLEMENTARY
1
4
2
65
7 8
3
Interior
Exterior
Exterior