3-2 Proving Lines Parallel Objective: use a transversal in proving lines parallel

Think back… Recall in Chapter 2 where we formulated converses of conditional statements. Examine this conditional statement: If a transversal intersects two parallel lines, then corresponding angles are congruent. You should be able to identify this as it is the Corresponding Angles Postulate. What would the converse of this conditional statement be?

Conditional: It’s converse:

Using the Converse of Corresponding Angles

Conditional: It’s converse:

Using Converse of Alternate Interior Angles

Conditional: It’s converse:

Using the Converse of Same Side Interior…

Conditional: It’s converse:

Using the Converse of Alt. Exterior Angles

Conditional: It’s converse:

Using Converse of Same Side Interior Angles

Compare the Postulate/Theorem with its Converse We use the original Theorems/Postulates to prove that my angles are Congruent (Corresponding, Alt. Int., Alt Ext.) or Supplementary (Same Side Int., Same Side Ext.) The Converses are used because we know the before information needed and we can prove the two lines Parallel.

Example 1:

Example 2: Apply Concepts

Example 2B: Apply Concepts

Example 2C: Apply Concepts

Example 3: Explain

Example 3: Continued

Create a Proof… Given: m<1 +m<3 = 180 Prove: l || m 3 l 1 2 m STATEMENTS REASONS

Analyze…