The Sum of the Interior Angles of Any Triangle

Consider this triangle made out of two-sided blue and yellow origami paper.
  • Drag the blue vertices to adjust the shape of the triangle.
First we will construct the altitude through the upper vertex.
  • Click the “Fold” button. This will color the lower left vertex yellow.
  • Drag the the yellow vertex until the “crease” passes through the upper vertex.
  • Click on the yellow triangle to “crease”.
  • Unfold the triangle completely.
The crease (the red doted line) is the altitude to the base. Why?
  • Drag each vertex of the triangle to the red point (the foot of the altitude).
What can you say about the sum of the interior angles of this triangle?
  • Click reset and experiment with different triangles.[list]