Here's a cute little geometric factoid that has something to do with one of the posts over at the 33rd Carnival of Mathematics. I'll leave it as a puzzle which post it belongs to...

Let ABC be any triangle in the Euclidean plane, and AD be any line. Form points A', B', and C' as the perpendicular projections of A onto BC, B onto AD, and C onto AD respectively. Then triangles ABC and A'B'C' are similar.



(Hint: in the post I have in mind, ABC is isosceles and A' is the midpoint of BC.)