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

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## 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 theorem 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