intercept theorem

Theorem.  If two intersecting lines are cut by parallel linesMathworldPlanetmath, the line segmentsMathworldPlanetmath cut by the parallel lines from one of the lines are proportional to the corresponding line segments cut by them from the other line.

The theorem may be condensed to the following form:

The intercept theorem has been known by the ancient Babylonians and Egyptians, but the first known proof is found in Euclid’s Elements.

Proof.  The areas of triangles, which have equal heights, are proportional to the bases of the triangles; if the bases are equal, then also the areas are equal.  These facts are used in the


of equalities. Q.E.D.

Title intercept theorem
Canonical name InterceptTheorem
Date of creation 2013-03-22 18:49:42
Last modified on 2013-03-22 18:49:42
Owner pahio (2872)
Last modified by pahio (2872)
Numerical id 8
Author pahio (2872)
Entry type Theorem
Classification msc 51-01
Classification msc 51M04
Related topic AreaOfAPolygonalRegion
Related topic SimilarTriangles
Related topic MidSegmentTheorem