Missing angles in a triangle leads us to the angle sum theorem which states that there are 180˚ in every triangle.  Really???  In EVERY triangle? How is this possible??  There are a lot of theorems in geometry that we TRY to prove to students, but perhaps it's difficult for everyone to make the connection.  The angle sum theorem in triangles though is a theorem that has a low floor and should allow more students to really internalize the idea.

Here are a few ideas for "proving" to students that there are 180˚ in the interior angles of EVERY triangle.