Today in Triangle Appreciation
Of course, it’s nice that the 10-10-12 triangle is isosceles. But what’s really cool is what happens when you drop the altitude from the top vertex!
It’s well known that in an isosceles triangle, the median and the altitude from the vertex are the same–this means that not only does this segment make a right angle (it’s the altitude), but it also divides the opposite side at its midpoint (it’s the median). So that segment creates two right triangles with hypotenuse 10 and side 6. Of course, the other side must be eight, since
Thank you, Pythagorean Theorem. So the 10-10-12 triangle is just two right triangles pasted together.
It’s not quite equilateral, but the 10-10-12 triangle is still pretty cool.