Triangle angle theorems are fundamental to geometry. They describe relationships between the angles of a triangle and are used in proofs, constructions, and real-world applications like architecture and engineering.
Triangle Angle Sum Theorem
The sum of the interior angles of any triangle is always 180°. This means if you know two angles, you can always find the third: angle C = 180° − angle A − angle B.
Exterior Angle Theorem
An exterior angle of a triangle equals the sum of the two non-adjacent interior angles (remote interior angles). This is a direct consequence of the angle sum theorem.
Triangle Congruence (SSS, SAS, ASA)
Two triangles are congruent if: SSS — all three sides are equal. SAS — two sides and the included angle are equal. ASA — two angles and the included side are equal. AAS — two angles and a non-included side are equal.
Explore with Interactive Diagrams
In VIZMath Geometry, select any theorem from the sidebar. Adjust the angle sliders to see how the theorem holds for any valid triangle configuration. Toggle proof steps to see the reasoning behind each theorem.