Triangle Congruence Sandwiches

I love teaching triangle congruence theorems.  It’s really one of my favorite parts of geometry!  But until this year, I just presented the theorems, and we practiced them.  Nothing exciting at all!  But this year, I had the awesome chance to experience a lesson taught by a fellow geometry teacher in our district.  At a Saturday PD day, Adrienne (who I get to call a friend now AND who finally joined Twitter!! (@Mrs_math_martin)) presented this lesson to us. I fell in love and was so excited to get to teach this to my math class. I knew it would really help them “get” the triangle congruence theorems.  It was just the spark this lesson needed!

I have no idea where the lesson originated from, but the activity we used can be found here:

I have a small class, so I split the students up into groups of two, and each group had to make one of each of the seven triangles.  This took all of one class period, and about 15 minutes of the period the next day.

*Note- if you use the linked assignment, one triangle calls for a side length of 12 inches.   You can either have 12 x 12 paper on hand, or you can have the students change the measurement to 11 inches.  We went with 11 inches because I just had plain 8.5×11 paper. Still worked perfectly! 🙂

After all of the triangles were made, we taped them to the board and had a pretty lengthy discussion about which “sandwiches” were appropriate for the restaurant to keep on their menu, and which were not.  Then I had the students guess how this related to triangles and they figured out that S stood for side and A stood for angle, and HL meant hypotenuse leg.  This lesson led beautifully into the introduction of the congruence theorems.  I still have the triangles taped up now as we have been referencing them throughout the week as we worked through the unit.


Nothing about this lesson was difficult to prepare and it wasn’t “flashy” by any means, but it did a wonderful job taking the congruence theorems and making them relevant for my students.  It is a keeper in my book!

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