Reflection: Connection to Prior Knowledge Triangle Sum Theorem and Special Triangles - Section 4: Prove the Triangle Sum Theorem


I thought proving the triangle sum theorem went really well this year.  It’s not like there were fireworks, but rather, flickering light bulbs that seemed to stay “on” for much longer. 

There was one few key phrase I used during this time that helped to reinforce the notion of proof, which I have used throughout the year: “convince a skeptic.” This phrase helped my students appreciate that despite the fact they investigated the angles of four different triangles (acute, obtuse, right, isosceles), tearing off the angles of each triangle, then gluing them so they are adjacent, this Visual Demonstration of a straight angle did not constitute a proof. 

Since this was the first “hefty” proof of the year, it was important to me that students consider multiple pathways to prove the angles of a triangle are supplementary.  I want my students to see multiple pathways because it helps them to make connections between the mathematics that drives the reasoning behind proof. Also, I think that students feel encouraged by the notion that if they don’t see one particular path, another one is waiting to be discovered.

The conversation in this lesson tends to follow a particular construction, create an auxiliary parallel line. Moreover, if students had used alternate interior angles in that construction, they tended to favor using alternate interior angles in their proof.   For this reason, if students favored alternate interior angles, I listened for and encouraged proofs that might have used corresponding and vertical angles, or consecutive (same side) interior angles.  This might sound inefficent, but being intentional about encouraging other ways to write the proof enables more of my students to achieve that “Aha!” light bulb moment. In addition, it encourages deeper engagement in mathematical practices. Giving students more time to wrestle with ideas and persevere, allows insight into the structure of a problem and prepares students to share and defend their ideas in conversation with others. 

  Connection to Prior Knowledge: Convince a Skeptic
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Triangle Sum Theorem and Special Triangles

Unit 7: Discovering and Proving Triangle Properties
Lesson 2 of 10

Objective: Students will be able to discover and prove the triangle sum theorem.

Big Idea: By investigating the angles of four different types of triangles, students conjecture about the interior angle sum of triangles and ultimately prove the triangle sum theorem.

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10 teachers like this lesson
Math, Geometry, Triangles, reasoning and proof, Triangle Sum Theorem, Triangle Congruence, triangle similarity
  85 minutes
triangle sum cropped image 1
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