Warm Up Week 1 1) If ∠ 1 and ∠ 2 are vertical angles, then ∠ 1 ≅ ∠ 2. State the postulate or theorem: 2) If ∠ 1 ≅ ∠ 2 and ∠ 2 ≅ ∠ 3, then ∠ 1 ≅ ∠ 3. 3) If ∠1 and ∠2 form a linear pair, then m∠1 + ∠2 = 180º.

Geometry 3.3 Day 1 I will prove and use results about parallel lines and transversals. P 15 Corresponding Angles If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent. 1 2 ∠ 1 ≅ ∠ 2

Alternate Interior Angles If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent. Theorem ∠ 3 ≅ ∠ 4

StepReason Ex 1 ∠ 1 ≅ ∠ 2 Prove: j ∥ k j k given ∠ 1 ≅ ∠ 3 Corresponding Angles Postulate ( P15 ) ∠ 3 ≅ ∠ 2 ∠ 1 ≅ ∠ 2 Transitive property of Equality

Consecutive Interior Angles If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles are supplementary. Theorem ∠ 5 + ∠ 6 = 180º

Alternate Exterior Angles If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent. Theorem ∠ 7 ≅ ∠ 8

m∠ 5 = 65º m∠ 6 angle Postulate or Theorem = m∠ 5 = 65º m∠ 7 = m∠ 5 = 115º m∠ 8 = m∠ 5 = 65º m∠ 9 = m∠ 7 = 115º Ex 2 measure

Do: 1 Assignment: Textbook Page 146, all m∠ 1 = 45º 5 1 What is the measure of ∠ 5?