Today in grade 9 and 10 we were working with some new technology.  Grade 10s were using the desmos geometry website to visualize some of our recent concepts like perpendicular bisector (médiatrice) and median (médiane).  In French these words are so similar that they are often mixed up.  We need a lot of practice and a good visual sense of what they are.

We could see that for isosceles triangles the “médiane” and “médiatrice” are the same for the non congruent side (it’s perpendicular to the side), and for an equilateral triangle all of the “médiane” and “médiatrice” are equal.

This program is great because you can construct something and then drag points around and see how the concepts are visually related.

Here’s a wordy question that we tried.  “Show algebraically that the perpendicular bisectors of the legs of a right triangle intersect at the midpoint of the hypotenuse.”

We analysed what the words told us, and what pictures came to mind.  We can show graphically that it is true.

And with some strategic calculations we can also verify algebraically.