Inscribe a Square in a Given Triangle


Consider the four vertices of a square. To have a square inscribed in a triangle, two of the square's vertices must lie on the same side of the triangle. Here are some examples:

Given a triangle, can we construct the inscribed square?


For the triangle shown above, there are three distinct inscribed squares. What conjectures can you make about number of inscribed squares for a given triangle? Is there any relation between the area of the inscribed square and the given triangle?


Presented by Alan Russell (Guest lecturer) from George Polya's How to Solve It.


Return to EMAT 4600/6600 Page