This morning we did a fun project involving a little triangle puzzle:

Here’s that project:

During the day I was just playing around with the triangles and found a couple of other fun ideas from geometry to show the kids.

First, an alternate proof that the two shapes have the same area. Almost a proof without words! It comes from the fact that the two shapes can come together to form a 6-8-10 triangle:

The next geometric idea involved a right triangle being inscribed in a circle:

It was a really nice surprise that there were other fun (and important!) geometric ideas that our shapes could be used for. We’ve used 3d printing before to play with 2d geometry – including triangles:

Inequalities and Mr. Honner’s Triangles

A Cool Geometry Problem Shared by Tina Cardone

A Follow Up to Our Tina Cardone Geometry Project

And also a fun project on using 3d printing to study an old AMC 10 problem:

Using 3d printing to help kids learn about algebra and 2d geometry

It really is amazing how much 3d printing can help students explore geometry.