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 $$BC$$.)