1. Topic: Parallel Lines Date: 2010 Objectives: SWBAT….
Determine the angle pair relationship when given two parallel lines cut by a transversal
Calculate the missing angle measurements when given two parallel lines cut by a transversal
Calculate the missing angle measurements when given two intersecting lines and an angle

2. Parallel Lines What are Parallel Lines?
Parallel lines are lines that lie in the same plane and do not intersect. A B C D
Symbol Form: AB II CD

3. Angles and Parallel Lines
A transversal is a line that intersects two other lines in two different points.
Note that 8 angles are formed. A B 1 2 3 4 C D 5 6 7 8

4. ACTIVITY Determine Angle Relationships formed by Parallel Lines Cut by Transversal1 2 3 4 5 6 7 8

5. S T O P !!!!
Distribute transparency sheets, parallel lines and record sheet for activity

6. Interior and Exterior AnglesB 1 2 3 4
Interior C D 5 6 7 8
Exterior
Interior angles are angles between the parallel lines
Exterior angles are angles outside the parallel lines

7. Alternate Interior AnglesB 3 4 C D 5 6
Alternate Interior Angles are equal if two parallel lines are cut by a transversal
So 3 and 6 are alternate interior angles
And they are CONGRUENT
and 4 and 5 are alternate interior angles

8. Alternate Exterior AnglesB 1 2 C D 7 8
Alternate Exterior Angles are equal if two parallel lines are cut by a transversal
So 2 and 7 are alternate exterior angles
And they are CONGRUENT
and 1 and 8 are alternate exterior angles

9. Corresponding Angles A B C D
When two lines are cut by a transversal, 4 pairs of corresponding angles are formed. A B 1 2 3 4 C D 5 6 7 8
Corresponding angles are congruent!

10. Vertical Angles
Vertical angles are always equal. And – you will always have vertical angles wherever two lines intersect! A B 1 2 3 4 C D 5 6 7 8

11. Interior Angles on the Same Side are SupplementaryB 3 4 C D 5 6
m4 + m6 = 180
m3 + m5 = 180

12. Exterior Angles on the Same Side are SupplementaryB 1 2 C D 7 8
m1 + m7 = 180
m2 + m8 = 180

13. Adjacent Angles creating a straight line are SupplementaryB 2 4 C D 7 8
m2 + m4 = 180
m7 + m8 = 180

14. Now how do we apply these Angle relationships?B C D 1 2 3 4 5 6 7 8
m 3 = 40˚. Find the m 5. Explain how
m 1 = 125˚. Find the m 8. Explain how
m 7 = 38˚. Find the m 4. Explain how you determined your answer

15. Summary Alternate Interior Angles are equal
Alternate Exterior Angles are equal
Corresponding Angles are equal
Vertical Angles are equal
Interior Angles on the same side are supplementary
Exterior Angles on the same side are supplementary
Adjacent Angles creating a straight line are supplementary

16. Algebraic Applications
Problem 1
In the accompanying diagram, l ll m.
Find the measure of the angle represented by (5x – 30)
(3x + 40)
(5x – 30) l m
SOLUTION:
The two angles are corresponding angles, so they are congruent
Set up the equation 3x + 40 = 5x and solve for x
(x = 35)
Once you know the value of x, substitute this value for x in 5x – 30
5(35) – 30 = 145

17. Algebraic Applications
Problem 2
In the accompanying diagram, l ll m.
Find the measure of the angle represented by (5x – 30)
(5x – 10)
(4x + 1) p q a
SOLUTION:
(x – 10) and a are corresponding angles, so they are congruent
But, first, we need to find the value of x
4x + 1 and 5x – 10 form a straight angle, so they are supplementary.
Set up the equation 4x x – 10 = 180 and solve for x
(x = 21)
Once you know the value of x, substitute this value for x in 5x – 10
5(21) – 10 = 95 Since a is congruent, we know a = 95.