Interactive
Theorems

Master IGCSE Geometry through real-time kinematics. Drag vertices to dynamically prove laws of the Incenter, Circumcenter, and Orthocenter.

Theorem_DB.exe

Trigonometric Laws

Equation 01

The Sine Rule

a / sin(A) = b / sin(B)

Utilized when presented with a "matching pair" (an angle and its corresponding opposite side). The ratio is continuous across all sides and equal to the diameter (2R) of the circumcircle.

Equation 02

The Cosine Rule

a² = b² + c² - 2bc · cos(A)

Applied to determine a third side given two sides and the included angle (SAS configuration), or extracting an angle when all three sides are known (SSS).

Equation 03

Area of a Triangle

Area = ½ · ab · sin(C)

A generalized formula for geometric area computation requiring only two sides and their included angle, bypassing the need for a perpendicular altitude.