3.2 – Proving Lines Parallel

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Presentation transcript:

3.2 – Proving Lines Parallel 1 2 m Postulate 3-2: Converse of Corresponding Angles Postulate: If two lines and a transversal form corresponding angles that are congruent, then the two lines are parallel.

Proving Lines Parallel 1 4 2 m Theorem 3-5: Converse of Alternate Interior Angles Theorem If two lines and a transversal form alternate interior angles that are congruent, then the two lines are parallel.

Proof of Theorem 3-5 (C of AIAT) l 3 1 m 2 Statements Reasons 1. 2. 3. 4.

Proving Lines Parallel 1 4 2 m Theorem 3-6: Converse of Same-Side Interior Angles Theorem If two lines and a transversal form same-side interior angles that are supplementary, then the two lines are parallel.

Proving Lines Parallel

Proving Lines Parallel 1 b 3 2 Theorem 3-7: Converse of Alternate Exterior Angles Theorem If two lines and a transversal intersects form alternate exterior angles that are congruent, then the two lines are parallel.

Proof of Theorem 3-7 (C of AEAT) 1 4 b 2 Statements Reasons 1. 2. 3. 4.

Proving Lines Parallel 1 b 3 2 Theorem 3-8: Converse of Same-Side Exterior Angles Theorem If two lines and a transversal intersects form same-side exterior angles that are supplementary, then the two lines are parallel.

Let’s Apply What We Have Learned, K? Find the value of x for which l || m l 40° m (2x + 6)°

You Try One! Find the value of x for which a || b a (7x - 8)° b 62°

Homework #12 Pg 137 #1-8, 10-21, 26, 28, 30

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