CTK Insights

I have recently posted a simple result picked from a very early (1930s) Moscow Math Olympiad for the middle schoolers: In triangle ABC, AE and BD are the altitudes to sides BC and AC, respectively. M is the midpoint of AB. Prove that MD = ME. Vladimir Nikolin, an elementary school teacher from Serbia, noticed that the statement leads to an engaging dissection of an acute triangle into 3 isosceles triangles with base angles being those of ΔABC and a triangle similar to the latter. He also shared his experience:

My target group is very young pupils (I call this underteen geometry), so my proofs must be the simplest one. That dissection is very useful for educational purposes, children love it, we made a model from hard paper of this triangle.

I could not be pleased more. A good teacher constantly seeks new ways to engage his/her students. It's a tough job to convince students of your enthusiasm unless this is how you really feel about math. The necessary attribute of being enthused by mathematics is doing mathematics. A few days earlier Vladimir submited elementary solutions to a few triangle problems. Now, this is a teacher who has something to share.

Related posts:

1. Dissection of Triangle into Rhombus by Hubert Shutrick
2. Sum of Squares in Equilateral Triangle
3. Our standards for school graduation