Illustrate That Interior Angles of a Triangle Sum to 180°

angles in a triangle sum to 180 degrees

You can illustrate the fact that the sum of the interior angles of a triangle is 180° by folding the triangle.


  1. Cut out a triangle of any shape. Orient the triangle so the longest side is the base.
  2. fold an altitudeFold the base onto itself so that the crease goes through the topmost vertex of the triangle. This crease will be the altitude of the triangle.
  3. fold a midsegmentFold the vertex down so it touches the base at the altitude. (This crease is a midsegment of the triangle).
  4. fold vertices to meetFold the other two vertices so that all three meet at the same point.
  5. See that all angles form a linear angle and sum to 180°.


  • 0406-n01A simpler version of this method involves tearing off the corners and putting them together so the vertices meet.