Proving The sum of the Interior Angles
in a Quadrilateral add up to 360°
How to prove the sum of the interior angles of a quadrilateral add up to 360°
- Given above is Quadrilateral ABCD and we want to prove the interior angles of this quadrilateral triangle adds up to 360°.
- First we join a diagonal, it does not matter which one you choose. As you can see I joined C to B.
- This new line helps create 2 new triangles ABS and BDC. As we already no from the section on triangles, a triangles interior angles add up to 180°.
- Therefore we now have two triangles within one Quadrilateral.
- 2(180°) = 360°
Interactive of Proof
- Drag Points A,B,C and D in any direction you want and notice how the angles will always add up to 360° regardless of the shape of the quadrilateral.