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.
Read more about this topic: Intercept Theorem
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The formulation was used as a motto by the English Nonconformist clergyman Richard Baxter (1615-1691)
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