Perpendicular in Right-Angled Triangle makes two Similar Triangles/Porism

Porism to Perpendicular in Right-Angled Triangle makes two Similar Triangles

In the words of Euclid:

From this it is clear that, if in a right-angled triangle a perpendicular be drawn from the right angle to the base, the straight line so drawn is a mean proportional between the segments of the base.

(The Elements: Book $\text{VI}$: Proposition $8$ : Porism)

Proof

Follows directly from Perpendicular in Right-Angled Triangle makes two Similar Triangles.

$\blacksquare$

Historical Note

This proof is Proposition $8$ 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