Proving Lines Parallel Section 3-2

Solve each equation. 1. 2x + 5 = a – 12 = x – x + 80 = x – 7 = 3x + 29 Write the converse of each conditional statement. Determine the truth value of the converse. 5. If a triangle is a right triangle, then it has a 90° angle. 6. If two angles are vertical angles, then they are congruent. 7. If two angles are same-side interior angles, then they are supplementary. Review:

Let’s review section 3-1. Corresponding Angles Postulate: If two parallel lines are cut by a transversal, then corresponding angles are congruent. Alternate Interior Angles Theorem: If two parallel lines are cut by a transversal, then alternate interior angles are congruent. Same-Side Interior Angles Theorem: If two parallel lines are cut by a transversal, then same-side interior angles are supplementary. Similar Theorems for the Alternate Exterior Angles Theorem and the Same- Side Exterior Angles Theorem were mentioned.

The CONVERSES of all of these postulates and theorems are true!

CONVERSE OF: Corresponding Angles Postulate If CONVERSE of: If two parallel lines are cut by a transversal, then corresponding angles are congruent.

CONVERSE OF: Alternate Interior Angles Theorem If CONVERSE of: If two parallel lines are cut by a transversal, then alternate interior angles are congruent.

CONVERSE OF: Same Side Interior Angle Theorem If CONVERSE of: If two parallel lines are cut by a transversal, then same-side interior angles are supplementary.

Here’s the Tricky Part! You need to remember which postulates/theorems were the originals and which ones are the converses. The originals start with: If two parallel lines are cut by a transversal, then... The converses start with: If ________ angles are ______, then the two lines must be parallel.

Let’s prove the Converse of the Alternate Interior Angles Theorem

Which lines, if any, must be parallel if m<1 = m<2? Which lines, if any, must be parallel if m<3 = m<4?

Find the value of x for which l || m.

Find the value of x for which a || b.

Two workers are painting lines for angled parking spaces. The first worker paints a line so that m<1 = 60. The second worker paints a line so that m<2 = 60. Explain why their lines are parallel. If the second workers uses <3, what should m<3 be for parallel lines? Explain.

Classwork:

Homework:

and 4 are supplementary Find the value of x for which a || b. 5. Find the value of x for which m || n. Suppose that m 1 = 3x + 10, m 2 = 3x + 14, and m 6 = x + 58 in the diagram above. Use the diagram and the given information to determine which lines, if any, are parallel. Justify your answer with a theorem or postulate.