Editing Thales's theorem (section)

{{Short description|On triangles inscribed in a circle with a diameter as an edge}}
{{For|the theorem sometimes called Thales' theorem and pertaining to similar triangles|intercept theorem}}
[[Image:Thales' Theorem Simple.svg|thumb|right|200px|Thales’ theorem: if {{mvar|{{overline|AC}}}} is a diameter and {{mvar|B}} is a point on the diameter's circle, the angle {{math|1=∠ ''ABC''}} is a right angle.]]

In [[geometry]], '''Thales's theorem''' states that if {{mvar|A}}, {{mvar|B}}, and {{mvar|C}} are distinct points on a [[circle]] where the line {{mvar|{{overline|AC}}}} is a [[diameter]], the [[angle]] {{math|∠ ''ABC''}} is a [[right angle]]. Thales's theorem is a [[special case]] of the [[inscribed angle theorem]] and is mentioned and proved as part of the 31st proposition in the third book of [[Euclid]]'s ''[[Euclid's Elements|Elements]]''.<ref>{{cite book |last=Heath |first=Thomas L. |date=1956 |title=The Thirteen Books of Euclid's Elements |volume=2 (Books 3–9) |edition=2nd |publisher=Dover |isbn=0486600890 |page=61 |url=https://archive.org/details/thirteenbooksofe00eucl/page/61}} Originally published by Cambridge University Press. 1st edition 1908, 2nd edition 1926. </ref> It is generally attributed to [[Thales of Miletus]], but it is sometimes attributed to [[Pythagoras]].