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The intercept theorem, also known as Thales' theorem (not to be confused with another theorem with that name), is an important theorem in elementary geometry about the ratios of various line segments that are created if two intersecting lines are intercepted by a pair of parallels. It is equivalent to the theorem about ratios in similar triangles. Traditionally it is attributed to Greek mathematician Thales.〔 ==Formulation== Suppose S is the intersection point of two lines and A, B are the intersections of the first line with the two parallels, such that B is further away from S than A, and similarly C, D are the intersections of the second line with the two parallels such that D is further away from S than C. # The ratios of any two segments on the first line equals the ratios of the according segments on the second line: , , # The ratio of the two segments on the same line starting at S equals the ratio of the segments on the parallels: # The converse of the first statement is true as well, i.e. if the two intersecting lines are intercepted by two arbitrary lines and holds then the two intercepting lines are parallel. However the converse of the second statement is not true. # If you have more than two lines intersecting in S, then ratio of the two segments on a parallel equals the ratio of the according segments on the other parallel. An example for the case of three lines is given the second graphic below. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Intercept theorem」の詳細全文を読む スポンサード リンク
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