Automedian triangle

Hey there kiddo! Today we’re going to learn about something called the automedian triangle.

So imagine you have a triangle. Three sides, three corners, right? Now let’s say you drew a line from one corner to the middle of the opposite side. That’s called the “median.” So if you did that for all three corners, you’d have three medians.

Great. So now let’s take those medians and draw in some more lines. We’re going to connect the places where they intersect the triangle. And when we’re done, we’ll have a new triangle!

This special triangle is called the automedian triangle. It’s special because each of its three corners is also the midpoint of one of the original triangle’s sides.

Why is it called “auto”median? Well, “auto” means self, like when you say “automatic” car or “autonomous” robot. These medians are “self” medians because they connect with the midpoint of the side they’re on.

Now, the cool thing about the automedian triangle is that it’s similar to the original triangle. That means if we compared the lengths of the sides and the sizes of the angles in the two triangles, they would be the same!

So the automedian triangle is just a special triangle you get by connecting the medians of any other triangle. It has really cool properties that make it similar to the original triangle, and it’s called “auto”median because it has things in common with itself!