1. Section 3-3 Proving Lines Parallel, Calculations.
Michael Schuetz

2. Theorem 3-4: Converse of the Corresponding Angles Theorem.If
Then l m 2 6
If two lines and a transversal form corresponding angles that are congruent, then the lines are parallel.

3. Theorem 3-5: Converse of the Alternate Interior Angles Theorem.If
Then l m 4 6
If two lines and a transversal form alternate interior angles that are congruent, then the lines are parallel.

4. Theorem 3-6: Converse of the Same-Side Interior Angles Postulate.If
Then l m 3 6
If two lines and a transversal form same-side interior angles that are supplementary, then the lines are parallel.

5. Theorem 3-7: Converse of the Alternate Exterior Angles Theorem.If
Then l m 1 7
If two lines and a transversal form alternate exterior angles that are congruent, then the lines are parallel.

6. Example 1, Identifying parallel lines
Which lines are parallel if and ? Justifies your answers?
Converse of the corresponding angles theorem l m 1 2 4 3 5 6 8 7 p q 9
Converse of the alternate interior angles theorem

7. p q l Example 2, Using Algebra
What is the value of x that makes p//q? Which theorem or postulate justifies your answer?
The converse of the Same-Side Interior Postulate tells us that to make p//q, then p q l
111˚
2x+9˚

8. Class work:
P. 160, #’s 7, 15, 16, 27, 31, 47

9. Section 3-3 Proving Lines Parallel, Proofs.

10. l m Proof of Theorem 3-5: Given: 2 Prove: l//m 4 6 Statements Reasons
2. Vertical angles are congruent
3. Transitive property
4. Converse of corresponding angles

11. l m Proof of Theorem 3-7: Given: 1 Prove: l//m 3 7 Statements Reasons
2. Vertical angles are congruent
3. Transitive property
4. Converse of Corresponding angles

12. l m Proof of Theorem 3-4: Given: 1 Prove: l//m 4 5 Statements Reasons
2. Angles 1 and 4 form a linear pair
3. Substitution
4. Converse of Same-Side-Interior angles.

13. Homework:
Worksheet