How I Teach Parallel Lines Converse Theorems

Parallel Lines Converse Theorems can be such a hard topic for students.  In my opinion, this is really the first time that students really have to pick apart a diagram and visualize what’s going on.

These teaching tips will help high school geometry students understand parallel lines proofs.  I love this free hands on activity!

When I start the lesson, I hand each student two cards.  One card says “the lines are parallel” the other says “corresponding angles are congruent” (or alternate interior, alternate exterior, same-side interior).  I tell the students to “put the cards in order to make a theorem”.  This takes them all of 2 seconds.  

How I Teach Parallel Lines Converse Theorems

Then, I remind them of what a converse is.  I have them switch the cards.  We talk about what is different.  This intro takes me less than 5 minutes, but it helps some of the kids a little.

How I Teach Parallel Lines Converse Theorems

Then, I usually use guided notes.  I’m not in love with the notes I use currently.  I would like to use some sort of foldable instead.  More and more I’m wanting to take the plunge into interactive notebooks.

After the lesson, I use this powerpoint.  It’s not fancy at all, but it gets the job done.  First, I project the slide onto the whiteboard.  
How I Teach Parallel Lines Converse Theorems
Then, I outline the angles in the question with a marker.  When you hit enter to move to the next slide, all of the unnecessary lines disappear.  Only the parallel lines are left for the students to see.  There are a bunch of problems for the students to practice.  I spend as much time as I can on this, because I think it really helps my students.  Even on tests, I can see where students outlined the angles to see which lines are parallel.

What do you do to help your students with this challenging topic?


  1. So glad I found your blog - I'm in the midst of this very lesson for Geometry. My students are struggling with the identification of the angles formed. My pacing guide states I should have my students understanding this concept in one lesson and move on to the converse…but I know my students are too confused to move on. So, one more day with parallel lines/transversals and angle relationships. I will definitely use your card idea when we start the converse section! Oh, I started using interactive math notes this year and it is a BIG hit with my students. Engagement has increased incredibly and students are much more protective of their notebooks - not one lost in 8 weeks of school! RJ

    1. My pacing guide only allots one day too. I just don't think it's quite enough time.

      I've been wanting to start interactive notebooks. I think I'm going to take the plunge next school year. There are two things that make me nervous to try them and students losing them is #1. I've been collecting ideas on a pinterest board, so that next year I'm ready!

    2. So….I tried something different for this lesson. After interactive notes, theorem cards and a worksheet, I still heard this today, "This makes no sense to me!" I can't see any angles." "It's too hard to figure out." "I should have failed Algebra so I wouldn't be in Geometry!@@" Yep - all due to parallel lines and congruent angles. So, I taped multiple diagrams of the parallel lines/transversals and made a 'Dance, Dance, Revolution' type game. Thought it could be fun but my first class just didn't engage. But, my 5th period loved it! Go figure! I'm going to change it to "Simon Says" tomorrow and reward winners with chocolate. RJ

    3. OMG, that is so cool! I may have to steal that! I hope your first class gets into it tomorrow, because that is a great opportunity for them to learn while being active. That will really help cement it in their brain.

  2. Wish I was in your class in highschool! Love your teaching style and your excitement for math!

    The Math Maniac


I love hearing from my readers. Thank you for taking the time to leave a comment!

Related Posts Plugin for WordPress, Blogger...
Powered by Blogger.
Back to Top