Proposition: 6.08: Perpendicular in RightAngled Triangle makes two Similar Triangles
(Proposition 8 from Book 6 of Euclid's “Elements”)
If, in a rightangled 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.
Modern Formulation
If in a rightangled 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 BYSA 3.0 Sources:
 Prime.mover and others: "Pr∞fWiki", https://proofwiki.org/wiki/Main_Page, 2016