Fundamental Theorem of Directly Similar Figures
- Author:
- Steve Phelps
Two figures are said to be similar when all corresponding angles are equal, and are directly similar when all corresponding angles are equal and described in the same rotational sense.
The blue F and the orange F denote two directly similar figures in the plane, related by a dilation and rotation centered at K. Corresponding vertices under the similarity are related by the light grey lines. The green F is also directly similar to both of the other F figures, and is related by a "weighted average" of the blue F and the orange F.
{green F} = (1-r) {blue F} + r {green F}