 Students will be able to ◦ Determine whether two lines are parallel ◦ Write flow proofs ◦ Define and apply the converse of the theorems from the previous section

 You can use certain angle pairs to determine if two lines are parallel

 What is the corresponding angles theorem?  If a transversal intersects two parallel lines, then corresponding angles are congruent  What is the converse of the corresponding angles theorem?  If two lines and a transversal form congruent corresponding angles, then the lines are parallel

 Which lines are parallel if <6 ≅ <7? ◦ m || l  Which lines are parallel if <4 ≅ <6 ◦ a || b

 If two lines and a transversal form alternate interior angles that are congruent, then the two lines are parallel

 If two lines and a transversal form same side interior angles that are supplementary, then the two lines are parallel.

 If two lines and a transversal form alternate exterior angles that are congruent, then the two lines are parallel.

 If corresponding angles are congruent, then the lines are parallel  If alternate interior lines are congruent, then the lines are parallel  If alternate exterior lines are congruent, then the lines are parallel  If same side interior angles are supplementary, then the lines are parallel

 In order to use the theorems relating to parallel lines, you must first prove the lines are parallel if it is not given/stated in the problem.  Even if lines appear to be parallel, you cannot assume they are parallel  Always assume diagrams are NOT drawn to scale, unless otherwise stated

 Third way to write a proof  In a flow proof, arrows show the flow, or the logical connections, between statements.  Reasons are written below the statements

 Given: <4 ≅ <6  Prove: l || m <4 ≅ <6 Given <2 ≅ <4 Vert. <s are ≅ <2 ≅ <6 Trans. Prop of ≅ L || m Converse of Corresponding Angles Thm. *You cannot use the Corresponding Angles Thm to say <2 ≅ <6 because we do not know if the lines are parallel

 Given: m<5 = 40, m<2 = 140  Prove: a || b  Start with what you know ◦ The given statement ◦ What you can conclude from your picture.  What you need to know ◦ Which theorem you can use to show a||b

 Given: m<5 = 40, m<2 = 140  Prove: a || b <5 = 40 Given <2 = 140 Given <5 and <2 are Supp. <s Def. of Supp. <s <5 and <2 are Same side Interior Angles Def. of Same Side Interior <s a || b Converse of Same Side Int. <s Thm

 You now have four ways to prove if two lines are parallel

 What is the value of x for which a || b?  Work backwards. What must be true of the given angles for a and b to be parallel?  How are the angles related? ◦ Same side interior ◦ Therefore, they must add to be 180

 What is the value of x for which a || b?  Work backwards. What must be true of the given angles for a and b to be parallel?  How are the angles related? ◦ Corresponding Angles ◦ Therefore, the angles are congruent

 Pg. 160 – 162  # 7 – 16, 21 – 24, 28, 32  16 Problems