Proof of the Sum of the Angles in a Triangle Theorem
We can prove the angles in a triangle add up to with the parallel line theorem and alternate angles.
If a line is drawn through one of the vertices, parallel to the opposite side, the other two angles in the triangle will be alternate angles with the other two angles at the chosen vertex that form a straight angle. This shows that the sum of the angles in a triangle is .
In the sketch you can move all three vertices.
If you click on one of the vertices, you will see the parallel line and the lines from the triangle forming a straight angle.