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

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.

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.

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.

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.

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

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˚

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

Section 3-3 Proving Lines Parallel, Proofs.

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

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

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.

Homework: Worksheet