Triangle of median

by

Hyeshin Choi

First I draw a triangle and find medians of the triangle. Then use three medians, I draw a new triangle.

This is how I draw a new triangle with medians. I took the shortest segment whose color is green and made circle. Then I took midium segment whose color is baby blue and draw a circle. Finally, I took the longest segment whose color is red and draw a circle. To get a triangle, connect the points where each circle meets.

Now I hide the circle so I can get original triangle and a new triangle using medians looks like below.

Now since these two triangles are not congruent I want to compare the area first. As you can see below the areas are not equal and the ratio is 1.333.

Now I compare the ratio of corresponding sides. As you can see below, the ratios are not same. This means that these two triangles are not similar.

Now I examined the relationship of tese two triangles' peremeters. As you can see, there is no relationship.