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| Theorem 8 |
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| If there are three or more parallel lines and the intercepts made by them on one transversal are equal, the corresponding intercepts of any transversal are also equal. |
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| l||m||n |
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| P is a transversal intersecting l,m and n at A, B and C respectively such that AB=BC. |
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| Q is another transversal drawn to cut l, m and n at D, E and F respectively. DE and EF are the intercepts made on q. |
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| DE = EF |
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| Draw a line through E parallel to p intersecting l in G, n in H respectively. |
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| AG||BE (given) |
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| GE||AB (by construction) |
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 AGEB is a parallelogram |
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| But AB=BC (given) |
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| From (i) and (ii), GE=EH |
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| Now compare triangles GED and EFH, |
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| GE=EH (proved) |
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| Hence the theorem is proved. |
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