Reflection: Station Rotation Proofs with Triangle Congruence Shortcuts - Section 4: Stations: Prove Properties of Special Triangles and Quadrilaterals with Congruent Triangles


As teachers, we know that there are often several ways to write a proof.  I often pose the following scenario to my students: if we wanted to walk from my classroom (a portable in the back of the school) to the library, is it true that there is more than one way to get there?  It’s fairly easy to get students to share out at least a few different paths they could take to walk to the library, some more efficient than others, some perhaps longer yet more scenic.


The Triangle Congruence Proof Menu is, to me, one of the first real salient times when students understand the idea that there can often be several correct ways to write the proof.  Because students move from one proof to another, they find themselves working with several different students, conversing about how they wrote their proof as they compare their ideas and work with each other.  They see that some proof paths are more efficient than others, or that some reveal insights they hadn’t first seen.  Contrast this to a situation in which students are handed a worksheet that features five pairs of triangles students must prove are congruent.  If/when students work individually through these proofs, they do not necessarily learn the valuable lesson that there are often multiple ways to be “right” (or even smart!) in math, or that if one path towards writing the proof doesn’t seem to work, they can always ditch it to try to find another that will lead them in the right direction.

  There really ARE a lot of different ways to write a proof!
  Station Rotation: There really ARE a lot of different ways to write a proof!
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Proofs with Triangle Congruence Shortcuts

Unit 7: Discovering and Proving Triangle Properties
Lesson 5 of 10

Objective: Students will be able to apply the triangle congruence shortcuts (SSS, SAS, ASA, AAS) to write proofs about special triangles and parallelograms that involve triangle congruence.

Big Idea: In stations, students can choose to work individually or with a partner to prove properties of special triangles and parallelograms using triangle congruence shortcuts.

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3 teachers like this lesson
Math, Geometry, Triangles, reasoning and proof, Triangle Congruence, triangle similarity
  110 minutes
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