## Friday, 30 October 2015

### MPM2D - Day 36: Triangle Centres

Now that my students have had the chance to practice finding equations of medians, altitudes and perpendicular bisectors, it was time to look at triangle centres. I started by giving them a piece of bright orange paper (it is the day before Halloween, after all) with a triangle on it, which I asked them to cut out.

Then I asked them to balance the triangle on the eraser end of a pencil and take note of the coordinates of the balance point.

Then I asked them how they could calculate the coordinates of the balance point and had them discuss ideas in their groups.

It was really interesting to see the groups that had thought to find the intersection of the medians react to the alternate, and much simpler, approach of finding the average of the x-coordinates and the average of the y-coordinates.

I told them that this point is called the centroid and is one of the triangle centres. Then I had them go to GeoGebra on the Chromebooks and we started constructing and investigating.

I asked them for conjectures on why the orthocentre is sometimes outside the triangle and they did a good job of figuring it out. Some needed a little hint so I added angle measures to my triangle.

There seemed to be the most confusion around perpendicular bisectors, but I think we cleared that up.

I showed them that I could construct a circle through all three vertices whose centre was the circumcentre of the triangle. Then I constructed line segments from the centre to each vertex and asked what was special about those segments.

I think they saw that this could be useful when they heard some examples.

Then we started the one example for the day, but only got this far.

So I asked if anyone would be upset if I held onto the homework until Monday after we finish this example. No one objected so they can work on their parabolic art over the weekend. Here is today's handout.