Proving Lines Are Parallel Chapter 3 Section 3.4 Proving Lines Are Parallel

Warm-Up State the converse of each statement. If <1 is a right angle, then m<1=90 If m<1 = 90, then <1 is a right angle. 2. If m<1 + m<2=180, then <1 and <2 are supplementary. If <1 and <2 are supplementary, then m<1 + m<2 = 180

When two lines are cut by a transversal so that… Corresponding angles are , then the lines are parallel Corresponding Angle Converse Alternate Interior angles are , then the lines are parallel Alt. Int. Angle Converse. Alternate Exterior angles are  , then the lines are parallel Alt. Ext Angle Converse Consecutive Interior angles are Supplementary , then the lines are parallel Con. Int. Angle Converse

Is It Possible to Prove That Lines P and Q Are Parallel Is It Possible to Prove That Lines P and Q Are Parallel? If So Explain How. Yes m1 = 124 (vert.  thm.) 1 and 56 are supplementary Cons. Int. Angle Converse 1 Yes 58 + 74 = 132 Corresponding Angle Converse

Is It Possible to Prove That Lines P and Q Are Parallel Is It Possible to Prove That Lines P and Q Are Parallel? If So Explain How. Yes m1 = 180 – 48 – 53 = 79 1 and 79 are congruent Alt. Int. Angle Converse 1

Find the Value of x That Makes p // q For p // q, Alt. Ext. Angles must be . 4x = 3x + 30 x = 30 For p // q, Cons. Int. Angles must be Supplementary. x + 3x + 24 = 180 4x + 24 = 180 4x = 156 x = 39

Find the Value of x That Makes p // q For p // q, Alt. Int. Angles must be . 2x + 50 = 5x – 10 60 = 3x 20 = x

Give the Choice or Choices That Makes the Statement True If two lines are cut by a transversal so that alternate interior angles ___________, then the lines are parallel. If two lines are cut by a transversal so that consecutive interior angles ___________, then the lines are parallel. Congruent Supplementary

Give the Choice or Choices That Makes the Statement True If two lines are cut by a transversal so that ____________________ are congruent, then the lines are parallel. alternate interior angles, Alt ext, corres

Complete the Two Column Proof Given Corres.  Postulate Given Transitive Alt. Ext  Converse

Write a two column proof Statements Reasons 1. Given 1. l // m, 1  2 2. 1  3 2. Corres.  Postulate 3. Transitive 3. 2  3 4. a // b 4. Corres.  Converse