Thales' Theorem states that if three points lie on a circle such that one of the segments they form is a diameter of that circle, then the angle at the third point is a right angle. Attributed to the ancient Greek philosopher Thales of Miletus, it is one of the oldest recorded results in geometry and a basic tool for constructing right angles with a compass and straightedge.
Facts
StatementIf A, B and C are distinct points on a circle such that the segment AC is a diameter of the circle, then the angle ABC is a right angle: any triangle inscribed in a semicircle with the diameter as one side is a right triangle. 1 Wikipedia's own lead notes the result is generally attributed to Thales of Miletus but sometimes to Pythagoras instead; no confirmable proof year survives for either attribution, ancient result. Classification
Statement FormCharacterization Theorem 1 Connections
Has Statement Form
In Branch
Proved By
Source Thales' Theorem (Wikipedia)
Sources
1. Thales' Theorem (Wikipedia)
Wikimedia FoundationLead section
It is generally attributed to Thales of Miletus, but it is sometimes attributed to Pythagoras.
Lead section
In geometry, Thales's theorem states that if A, B, and C are distinct points on a circle where the line AC is a diameter, the angle ∠ ABC is a right angle.
Proved By: Euclid, Lead
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 Elements.
View the Source Reader Challenges (0)
No disputes yet. Spotted an error or a better source? Open the first one.
Sign in to dispute this or suggest a correction.