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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.
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 ]
The latter two can be done with a construction based on the intercept theorem. A slightly less elementary construction using these tools is based on the geometric mean theorem and will construct a segment of length from a constructed segment of length . It follows that every algebraically constructible number is geometrically constructible, by ...
Intermediate value theorem ; Intercept theorem (Euclidean geometry) Intersecting chords theorem (Euclidean geometry) Intersecting secants theorem (Euclidean geometry) Intersection theorem (projective geometry) Inverse eigenvalues theorem (linear algebra) Inverse function theorem (vector calculus) Ionescu-Tulcea theorem (probability theory)
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Garfield's proof of the Pythagorean theorem; H. Hjelmslev's theorem; ... Intercept theorem; M. Midpoint theorem (conics) Mohr–Mascheroni theorem; N. Newton's ...
The midpoint theorem generalizes to the intercept theorem, where rather than using midpoints, both sides are partitioned in the same ratio. [1] [2] The converse of the theorem is true as well. That is if a line is drawn through the midpoint of triangle side parallel to another triangle side then the line will bisect the third side of the triangle.