Kids passionate about triangle proofs!


Yes, the title is a bit like “man bites dog”, but it really happened! #MTBoS30

My fifth period is a group of the most interesting, undisciplined, rowdy bunch you will ever meet, and when they get stuck on something, they are passionate about defending their position. Tuesday that defense had to do with a simple triangle proof.

The image was similar to the one above: two slightly overlapping triangles, ABC and XYZ. The given: angle A is congruent to angle Z and segment AB is congruent to segment ZY. The question asked students to provide the one other statement that would prove congruency.

The students leapt into defense mode with both feet, convinced that the answer was segment BC congruent to segment XY.

Two students were convinced they were right. Two other students went crazy trying to convince them (and the rest if the class) that a pair of congruent angles was the solution. One young man was carrying around a piece of paper and illustrating his position to anyone who would listen. Postulates were being quoted, and terms like SAS and SSA and SSS were flying about like paper airplanes! Wow! I ‘m looking for the next argument – I wish they would be as passionate about math everyday!

What is your solution to this problem? How would you defend it?

My passionate, argumentative students were taking the image at face value. They also weren’t reading the question correctly. This was a great problem from the standpoint of “what error(s) are we making? What assumptions? It was also a great segue into a brief reminder of ambiguous triangles and why SSA is NOT a postulate!

I was thrilled – It was a proud moment in proof-dom!!! I think we will argue about probabilities tomorrow!