The Department of Mathematics and Science Education

tiffani c. knight

First, I constructed a triangle and then its medians. The sides of the second triangle have the same length as the medians of the first triangle. Let’s see if there is a relationship between the two triangles.

Well, they did not have the same area, nor did they have the same perimeter. However, they were very close to being equal. There must be some relationship between the two or there would be no point to this problem besides the construction of a triangle with side lengths that are equivalent to the medians of another triangle. That in itself is an activity that my students would have fun doing. I guess I should explore the ratios of the areas and perimeters…I will come back to do that.

I read somewhere that the triangle created with medians will have an area ¾ of the area of the triangle from which it was created. Let’s see if this is true. So, is 5.17 ¾ or 75% of 6.91? 75% of 6.91 came out to be 5.18. This is pretty darn close and I will attribute the slight error to rounding that took place in the calculator that I used.