Having trouble teaching the concepts of Circumcenter, Incenter, Centroid and and Orthocenter? Are you students getting frustrated with all of the different steps? After teaching this lesson for many years in a row I have noticed that even as a teacher I have trouble remembering which segments go with which concurrent point. As a result I have come up with the acronym "PAMACICO" which when written as two columns helps the kids memorize which pieces go together. P goes with C which means that Perpendicular bisectors create Circumcenters. Angle bisectors create Incenters. Medians create Centroids and Altitudes create Orthocenters. I usually tell some big long story about one of the students having a "girlfriend" named Pamacico and go from there. I talk about it in the same way that Trig teachers use Soh-Cah-Toa.
Aside from the Acronym I have created this quick activity for the kids to explore the properties of these points on Geometer's Sketchpad.
The directions are streamlined to get the activity done as quickly as possible. It usually takes me a normal class period (42 minutes) to go over all four points.
The last page includes a few very basic follow up questions that would be good for an introductory lesson. A complete key is also attached.
*If you do not have Geometer's Sketchpad you can use programs like GeoGebra for similar results. The directions might be slightly different for different programs. This is specifically written for Geometer's Sketchpad.
I will be uploading more intricate lessons and notes that go with this activity very soon. Please check back soon. Also, please check out my other math lessons that might be helpful to you.
If you like this download I would appreciate any positive feedback you would be willing to leave.
Thanks and happy teaching!
Geometer's Sketchpad Activity for Concurrent Points in a Triangle
by Dana Burrows
is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License