Demonstrate that the angle sum of a triangle is 180° and use this to find the angle sum of a quadrilateral (ACMMG166)
- using concrete materials and digital technologies to investigate the angle sum of a triangle and quadrilateral
Source: Australian Curriculum, Assessment and Reporting Authority (ACARA)
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.
- Cut out a triangle. Tear the corners off and place them together so that they form a straight angle.
- Draw a number of different triangles. Measure the angles and check that their sum is 180°. Set squares are excellent examples of triangles.
- Cut out a triangle. Fold it without tearing it to demonstrate that the three interior angles form a straight angle.
This third demonstration is close to a proof.