My favorite elementary geometry proof is that medians divide a triangle into 6 triangles having equal area.
I’m a tiny bit disappointed that our Geometry book covers this theorem before it covers Ceva’s theorem because having to assume that the medians intersect in a single point is a bit of a shame. No matter, though, I’ve always found it amazing that you can prove this nice fact just from the area formula for a triangle. It is a really nice example of mathematical ideas for kids.
I broke the proof into three parts of about 3 minutes each. Not much commentary is necessary as the proof really stands on its own. This sequence shows another example of why I love talking about math with my kids.
Mike's Math Page 