1. Section 3-2 Properties of Parallel Lines, Calculations.
Michael Schuetz

2. Postulate 3-1: Same-Side Interior Angles Postulate.
If l//m
Then l m 1 2 4 3 5 6 8 7
If a transversal intersects two parallel lines, then same-side interior angles are supplementary

3. Theorem 3-1: Alternate Interior Angles Theorem. (AIA)
If l//m
Then l m 1 2 4 3 5 6 8 7
If a transversal intersects two parallel lines, then alternate interior angles are congruent.

4. Theorem 3-2: Corresponding Angles Theorem. (Corr )
If l//m
Then l m 1 2 4 3 5 6 8 7
If a transversal intersects two parallel lines, then corresponding angles are congruent.

5. Theorem 3-3: Alternate Exterior Angles Theorem. (AEA)
If l//m
Then l m 1 2 4 3 5 6 8 7
If a transversal intersects two parallel lines, then Alternate exterior angles are congruent.

6. p q l m Example 1, Angle Measure
What are the measures of angles 3 and 4? Which theorem or postulate justifies your answer?
AIA Theorem l m 1 2 4 3 5 6 8 7 p q
105˚
Same-Side Interior Postulate

7. p q l Example 2, Angle Measure
What is the value of y? Which theorem or postulate justifies your answer?
Same-Side Interior Postulate tells us that p q l y˚
80˚
40˚

8. Classwork:
P. 153, #’s 7, 12, 15, 16, 19, 20

9. Section 3-2 Properties of Parallel Lines, Proofs.

10. l m Proof of Theorem 3-1: AIA 4 3 6 Given: l//m Prove: Statements
Reasons
1. Given
2. Supplementary Angles
3. Same-Side Interior Angles Postulate
4. Transitive Property of Equality
5. Subtraction Property of Equality
6. Definition of Congruence

11. Proving an angle relationship
Given: l//m
Prove:
are supplementary l m 1 5 8 7
Statements
Reasons
1. Given
2. If lines are //, then Corr
have equal measure.
that form a linear pair are suppl.
5. Def. of suppl.
6. Substitution Property
7. Def. of suppl.

12. Homework:
P. 153, #’s 10, 11, 25, 26.