Reflection: Flexibility Walking Around a Triangle - Section 2: Student Work Time

This summary covers a lot of content, but it connects nicely and will help them piece together the ideas in their investigation. First, talk to them about interior angles and the notion of similarity. If we know 2 angles, we know the third angle because the third angle must add up to 180. This is true regardless of triangle size. The goal is to try a few problems where students find the missing angle and then compare the results to a triangle of the same size, smaller and larger. I recommend using a triangle that is easy to draw for this part of the discussion (I prefer using Pythagorean triplets here).

You could also craft a few problems from this set, just click the links to the 10 math questions found in Triangle Resource. Mention the concept of scale factor, size and area and then transition to the exterior observations. You will most likely have a lot to share from you work during the middle part of class and should quote specific things you heard partners discuss, but you could lead the conversation if needed. Simply choose a triangle from the class, label the exterior angles and discuss pattern findings. Lean the discussion toward the exterior angle theorem first and then finish with the exterior angle sum. Discuss the logic as to “why” the exterior angle sum is 360. I like to tape a path on the floor in bright painters tape. Have a student stand at a vertex (or you could stand or have many students form a fun conga line to music, etc) and walk around the triangle until they return to their exact starting point. The idea is that in order to get back to the same location and in order to be facing the same way, the student would have had to turn 360 degrees. This idea could then extended to higher sided polygons.

Closing this Lesson
Flexibility: Closing this Lesson

Walking Around a Triangle

Unit 5: Lines, Angles, and Algebraic Reasoning
Lesson 8 of 16

Big Idea: In this investigation we open with AA criterion for triangles and help students discover that the exterior angles of a triangle (and any polygon) must always add to 360.

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Standards:
Subject(s):
Math, Proofs, Geometry, exterior angle, transversals, protractor, interior angles, 8th grade
55 minutes

Shaun Errichiello

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