1. Properties of Lines and Transversals
Unit 3

2. Lines Cut by a Transversal
Unit 3: Properties of Lines and Transversals

3. Two Lines Cut by a Transversal
Angles 4 and 5 are on the inside of lines j and k and are on the same side of the transversal t, so they are _____________________. Name another pair:
Angles 4 and 6 are on the inside of lines j and k and are on opposite sides of the transversal t, so they are _____________________. Name another pair:
Angles 1 and 8 are on the outside of lines j and k and are on the same sides of the transversal t, so they are _____________________. Name another pair:
Same Side Interior Angles
Alternate Interior Angles
Same Side Exterior Angles

4. Two Lines Cut by a Transversal
Angles 1 and 7 are on the outside of lines j and k and are on opposite sides of the transversal t, so they are _____________________. Name another pair:
Angles 1 and 5 hold the same position in relation to their respective lines and the transversal (upper left or northwest corner) so they are ____________________. Name another pair:
Alternate Exterior Angles
Corresponding Angles

5. Two Lines Cut by a Transversal
Name all linear pairs (add up to 180˚) in the figure:
Name all vertical angles (congruent) in the figure:
Angles 1and 4, 4 and 3, 3 and 2, 1 and 2, 5 and 8, 8 and 7, and 6, 5 and 6
Angles 1 and 3, 4 and 2, 8 and 6, 5 and 7

6. Parallel Lines Cut by a Transversal
What is special about the alternate interior angles when the two lines cut by a transversal are parallel?
What is special about the same side interior angles when the two lines cut by a transversal are parallel?
What is special about the alternate exterior angles when the two lines cut by a transversal are parallel?
They are congruent
They are supplementary (add up to 180˚)
They are congruent

7. Parallel Lines Cut by a Transversal
What is true about the same side exterior angles when the two lines cut by a transversal are parallel?
 What is true about the corresponding angles when the two lines cut by a transversal are parallel?
They are supplementary (add up to 180˚)
They are congruent

8. Construction of a line parallel to a given line through a point not on the line

9. Investigating Parallel Lines and Angle Pairs
Unit 3: Properties of Lines and Transversals

10. Investigating Parallel Lines and Angle Pairs
Postulate: Statement that is assumed to be true.
Theorem: Statement that is priven to be true.

11. Investigating Parallel Lines and Angle Pairs

12. Investigating Parallel Lines and Angle Pairs

13. Guided Practice

14. Guided Practice

15. Investigating Parallel Lines
Unit 3: Properties of Lines and Transversals

16. Investigating Parallel Lines
Definition: When the conditional statement and converse are both true. (bi-conditional statement)

17. Investigating Parallel Lines

18. Euclid’s Parallel Postulate: If there is a line and a point not on the line, there exists exactly one line through the point that is parallel to the given line.

19. Guided Practice