Proposition: 6.08: Perpendicular in Right-Angled Triangle makes two Similar Triangles
(Proposition 8 from Book 6 of Euclid's “Elements”)
If, in a right-angled triangle, a (straight line) is drawn from the right angle perpendicular to the base then the triangles around the perpendicular are similar to the whole (triangle), and to one another.
![fig08e](https://github.com/bookofproofs/bookofproofs.github.io/blob/main/_sources/_assets/images/euclid/Book06/fig08e.png?raw=true)
Modern Formulation
If in a right-angled triangle a straight line is drawn from the vertex of the right angle to the hypotenuse, then the resulting two triangles are similar.
Table of Contents
Proofs: 1 Corollaries: 1
Mentioned in:
Proofs: 1 2 3 4 5 6 7 8 9 10
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References
Adapted from (subject to copyright, with kind permission)
- Fitzpatrick, Richard: Euclid's "Elements of Geometry"
Adapted from CC BY-SA 3.0 Sources:
- Prime.mover and others: "Pr∞fWiki", https://proofwiki.org/wiki/Main_Page, 2016