Student resources icon

Investigating the interior angles of a triangle

The first important result about a triangle is that the sum of its three interior angles is always 180°. There are a number of ways to demonstrate this result.

  1. Cut out a triangle. Tear the corners off and place them together so that they form a straight angle.
    Triangle ABC with interior angles alpha at A, beta at B and gamma at C.
    Detailed description
  2. Draw a number of different triangles. Measure the angles and check that their sum is 180°. Set squares are excellent examples of triangles.
    Two triangles each ABC with interior angles marked.
    Detailed description
  3. Cut out a triangle. Fold it without tearing it to demonstrate that the three interior angles form a straight angle.
    Two triangles.
    Detailed description

This third demonstration is close to a proof.