If parallel lines are cut by a transversal, eight angles are formed that have specific relationships. Corresponding angles are congruent. Alternate interior angles and alternate exterior angles are congruent. Interior angles and exterior angles on the same side of the transversal are supplementary. The document provides examples of angle measurements that illustrate these properties and includes practice problems asking to determine angle measures using these relationships.

1. ANGLES FORMED BY PARALLEL
LINES CUT BY TRANSVERSAL
8/28/2012 1
MAY P. BUNDANG
ZNHS

2. tt t
SET A
t is a transversal
t
t
t
SET B
t is not a transversal

3. Transversal is a line
that intersects two
or more lines at
different points

4. If parallel lines are cut by a transversal, then eight angles and pairs of
angle are formed.
1 2 l
5
4 3
n
7 8
6
m
l and m are parallel lines (l // m)
n is a transversal

5. Corresponding angles
– a combination of an exterior angle and an interior angle
which are non-adjacent but lie on the same side of the transversal
1 2 l
5
4 3
n
7 8
6 m

6. • Interior angles on the same side of the transversal
1 2 l
5
4 3
n
7 8
6 m
Interior angles
1 2 l
5
4 3
n
7 8
6 m
• Alternate interior angles

7. • Exterior angles on the same side of the transversal
1 2 l
5
4 3
n
7 8
6 m
Exterior angles
2 l
5
4 3
n
7 8
6 m
• Alternate exterior angles

8. Observe the measures of the angle pairs.
n
1 2 l
5
4 3
7 8
6
m
110o
70o
110o
110o
110o
70o
70o
70o

9. Pairs of Angles Measurement
•Corresponding Angles
1 and 5
4 and 7
2 and 6
3 and 8
110 o
70o
70o
110 o
•Alternate interior angles
3 and 5
4 and 6
110 o
70o
•Interior angles on the same side of the transversal
4 and 5
3 and 6
4 = 70 o and 5 = 110o
6 = 70 o and 3 = 110o
•Alternate exterior angles
1 and 8
2 and 7
110 o
70o
•Interior angles on the same side of the transversal
1 and 7
2 and 8
1= 110 o and 7 = 70o
8= 110 o and 2 = 70o

10. What did you observe with the measurements
of the pairs of angles?
a. Corresponding angles?
b. Alternate interior angles?
c. Interior angles on the same side of the
transversal?
d. Alternate exterior angles?
e. exterior angles on the same side of the
transversal?

11. Answers:
• Corresponding angles are congruent.
• Alternate interior angles are congruent.
• Interior angles on the same side of the
transversal are supplementary.
• Alternate exterior angles are congruent.
• Exterior angles on the same side of the
transversal are supplementary.

12. Given: l // m
n
1
11
l
5
43
78 6
m
p
2
10
16 13
12 9
15 14
1. Find the measure of the other numbered angles, if measure of
a. 1 is 68o
b. 3 is 95o

13. 2. If measure of 6 = 5x – 10 and measure of 3 = 8x - 34,
a. what is x?
b. find the measure of the angles.
r
21
s
f43 7 8
65

14. Conclusion:
If two lines are cut by a transversal then
• corresponding angles are congruent.
• alternate interior angles are congruent.
• interior angles on the same side of the
transversal are supplementary.
• alternate exterior angles are congruent.
• exterior angles on the same side of the
transversal are supplementary.

15. 2. If measure of 2 = x + 20 and measure of 5 = 4x - 50,
a. what is x?
b. find the measure of the angles.

16. 4x + 15
n
1
11
l
5
43
78 6
m
p
2
10
16 13
12 9
15 14
3X - 20
X + 40 6X - 25
3. Solve for x and find the measure of the angles.