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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. 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 . [ 1 ]
A special case of the theorem is Thales's theorem, which states that the angle subtended by a diameter is always 90°, i.e., a right angle. As a consequence of the theorem, opposite angles of cyclic quadrilaterals sum to 180°; conversely, any quadrilateral for which this is true can be inscribed in a circle.
The intercept theorem, also known as Thales's theorem, basic proportionality theorem or side splitter theorem, is an important theorem in elementary geometry about the ratios of various line segments that are created if two rays with a common starting point are intercepted by a pair of parallels.
Download as PDF; Printable version; In other projects Wikidata item; ... Thabit ibn Qurra's theorem (amicable numbers) Thales's theorem ; The duality theorem ...
By the power-of-a-point theorem, the product of lengths PM · PN for any ray PMN equals to the square of PT, the length of the tangent line segment (red). No tangent line can be drawn through a point within a circle, since any such line must be a secant line. However, two tangent lines can be drawn to a circle from a point P outside of the circle.
Thales' theorem implies that if the circumcenter is located on the side of the triangle, then the angle opposite that side is a right angle. [21] If the circumcenter is located inside the triangle, then the triangle is acute; if the circumcenter is located outside the triangle, then the triangle is obtuse. [22]
Ebook version, in PDF format, full text presented. Trigonometry by Alfred Monroe Kenyon and Louis Ingold, The Macmillan Company, 1914. In images, full text presented. Trigonometry FAQ; Trigonometry on Mathwords.com index of trigonometry entries on Mathwords.com; Trigonometry on PlainMath.net Trigonometry Articles from PlainMath.Net
According to some historical sources the Greek mathematician Thales applied the intercept theorem to determine the height of the Cheops' pyramid. The following description illustrates the use of the intercept theorem to compute the height of the Cheops' pyramid. It does not however recount Thales' original work, which was lost.