Similar Polygons are composed of Similar Triangles/Porism

Porism to Similar Polygons are composed of Similar Triangles

In the words of Euclid:

Similarly also it can be proved in the case of quadrilaterals that they are in the duplicate ratio of the corresponding sides. And it was also proved in the case of triangles; therefore also, generally, similar rectilineal figures are to one another in the duplicate ratio of the corresponding sides.

(The Elements: Book $\text{VI}$: Proposition $20$ : Porism)

Proof

Follows immediately from Similar Polygons are composed of Similar Triangles.

$\blacksquare$

Historical Note

This proof is Proposition $20$ of Book $\text{VI}$ of Euclid's The Elements.

Sources

• 1926: Sir Thomas L. Heath: Euclid: The Thirteen Books of The Elements: Volume 2 (2nd ed.) ... (previous) ... (next): Book $\text{VI}$. Propositions