28.	+Converse+Consecutive+Angles+Theorem

__ Converse Consecutive Interior Angles Theorem __  By: Steven Rak and Craig Mileham  The converse consecutive interior angles theorem states that if two lines are cut by a transversal so that a pair of consecutive interior angles add up to 180, then the lines are parallel. The goal is to prove lines are parallel through the consecutive interior angles theorem. If we are able to prove that the consecutive interior angles add up to 180 in a sketch, then we can prove the lines are parallel.  Sample Problems: Refer to Diagram to the Right for Problems 1 through 3 1) If angle 2 is 60 degrees and angle 5 is 110 degrees, can you conclude that the lines //l// and //k// are parallel? 2) If angle 3 is 40 degrees and angle 8 is 140 degrees, can you conclude that the lines //l// and //k// are parallel?

//Answers:// 1) No 2) Yes 3) Yes

Help: When trying to see if the converse consecutive interior angle theorem applies, look to see if the pair of consecutive interior angles are supplementary. Remember that supplementary means that the sum of the angles add up to 180.

Remember to make sure that the angles you are looking at are on the same side of the line, not the opposite sides. This is a common mistake.

Remember that Alternate Interior Angles are formed when a transversal, cuts through two parallel lines.



Wed Pages of Our Topic: 1) [|Postulate and Theorem Definitions] 2) [|Theorem and Property Sheets] 3) [|Help with Theorems]

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