# 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.

## Proof

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

$\blacksquare$

## Historical Note

This theorem is Proposition $8$ of Book $\text{VI}$ of Euclid's The Elements.