Isosceles Triangle I

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When does the triangle ABC become isosceles?

To begin we have the students construct the animation. We note that the starting and ending triangles are isosceles. We ask if there might be other times at which the triangle ABC is isosceles. We start with the students playing with the animation and they quickly find two possibilities, one quite early , and another much later .  

Okay: time for some calculation. Check out all possible cases. This requires a calculation of the squares of the lengths of each of the three sides of the red triangle. It turns out that there 6 possible cases in all, one of which requires an extension of the diagram.

This is a good Grade 10 problem. It assumes that the students can find the distance between any two points in the plane.