intercept theorem

Also known as basic proportionality theorem, Thales's theorem, side splitter theorem

theorem on ratios of line segments formed when 2 intersecting lines are cut by a pair of parallels

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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. 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. A mechanical device which produce geometricaly-similar shapes is known as a pantograph.

Formulation of the theorem