Question

if there are three parallel lines and the intercepts made by them on a transversal are equal in length , prove that the intercepts on any other transversal are also equal in length​

Answer 1

Equal Intercept Theorem

The theorem states if a transversal makes equal intercepts on three or more parallel lines, then any other line cutting them will also make equal intercepts. It means that given any three mutually perpendicular lines, a line passing through them forms intercepts in the corresponding ratio of the distances between the lines.

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For example, Suppose there are three lines, l, m and n. Keep the distance between l–m twice than the distance between m–n. So any line passing through them, the intercept made by l-m on the line is twice the intercept made by m-n.