Triangle centers and the segments that create them easily become an exercise in memorization, without the help of engaging applications like this lesson. Here the class investigates the measure of center that is equidistant to the three points of a triangle (the circumcenter). Not only do they physically develop that this point is found from the perpendicular bisectors of the sides, but they then back it up with mathematical justifications. A great activity for illustrating exactly why these measures of center are so important.

Concepts

perpendicular bisectors, center, triangle properties

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Additional Tags

math

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Instructional Ideas

• Add as an enrichment activity into the standard memorization of the different centers of triangles and the segments that create them
• Ask what the other measures of center (orthocenter, incenter, centroid) would mean in relation to the physical context of the problem
• Extend by adding additional point locations, and investigating the best hydrant placement for those shapes

Classroom Considerations

• Be aware that some learners might know the perpendicular bisector and circumcenter trick while some might not, making for uneven completion rates
• Suggested teaching method in activity has the class using geometry modeling software instead of folding actual paper
• If using black and white copies, the instructions do reference colors in the images

Pros

• Real-world application of triangle properties
• Learners develop key conclusions from physical manipulation of the problem

Cons

• In the first sentence, the word from is misspelled (form)
• Teaching notes and answer key not separated from class task assignment

Common Core

HSG-C.A.3