Sunday, October 23, 2011

Triangle Centers

I'm attempting to incorporate triangle centers with constructions. locus, and parts of coordinate geometry, because they all go together anyway. This is one of the things I love about Geometry - there are many topics, but they all relate to each other.

Some of my questions are exact replicas of those found in Exeter Math Book 2. I'll attach all the documents I used, and I know they are imperfect. But this is the basic progression:

Incenter
Where is a point that is equidistant from all sides? Conjecture that there is such a point on Nspire.



Figure out how to construct it by pouring salt on triangles.



Circumcenter
After doing some problems to review that there is such a thing as the Pythagorean Theorem...Where is a point that is equidistant from all vertices? Use coordinate geometry to see that there is such a locus of points on the coordinate grid.


Centroid
After a detour into deriving the midpoint formula... Where is a point that is the center of gravity in a triangle? Use area and coordinate geometry to dissect a triangle into two equal areas.



Demonstrate center of gravity by demonstrating that the triangle will balance on that point.

video


Where is the intersection of the altitudes? This point is not interesting, so get through it as quickly as possible. But take the opportunity to teach what an altitude is.

Then there's an Nspire document with a summative review sheet so that they can keep straight the four different, confusing kinds of triangle centers.

Next we are going to do the famous locus scavenger hunt, after a day of basic locus notes, which will allow me to basically skip the whole pointless locus unit altogether.

And then I think I am going to have the children make their own locus-based scavenger hunt for the towns of Fayetteville and Manlius, for the fun, and for the backwards learning. Though I don't happen to have those documents prepared yet.