Intercept theorem
On ratios of line segments formed when 2 intersecting lines are cut by a pair of parallels / From Wikipedia, the free encyclopedia
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This article is about the theorem about the ratios of various line segments. For the special case of the inscribed angle theorem, see Thales's theorem.
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. It is equivalent to the theorem about ratios in similar triangles. It is traditionally attributed to Greek mathematician Thales. It was known to the ancient Babylonians and Egyptians, although its first known proof appears in Euclid's Elements.