# A Visual Proof of Thales's Intercept Theorem

A Visual Proof of Thales's Intercept Theorem

Consider an arbitrary triangle with sides , , . Extend to and to to form a second triangle with third side parallel to . Then the lengths of the sides satisfy the relations == and hence =, =, =. In other words, the line segments that are created if two intersecting lines are intercepted by a pair of parallels are proportional.

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You can drag the two red points.