Theorem about the Sum of Angles in a Triangle
One of the most important theorems in all of geometry
📐 Introduction
This is one of the most important theorems in geometry. It tells us something remarkable about the angles inside any triangle — no matter how big, how small, or what shape it is.
Theorem: The sum of the interior angles of a triangle equals $180°$.
In symbolic form, for any triangle $ABC$:
$\angle A + \angle B + \angle C = 180°$
Acute Triangle
All angles less than $90°$
$60° + 70° + 50° = 180°$ ✓
Right Triangle
One angle equals $90°$
$90° + 45° + 45° = 180°$ ✓
Obtuse Triangle
One angle greater than $90°$
$120° + 35° + 25° = 180°$ ✓
This theorem is true for ALL triangles regardless of type or size!
🔄 Interactive: Drag the Vertices and Watch the Angles!
Drag points $A$, $B$, or $C$ to change the triangle. Notice that the sum always stays at $180°$.
Interactive visualization — available in the full lesson