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# If there are three or more parallel lines and the intercepts made by them on one transversal are equal, then the corresponding intercepts by any other transversal are also equal.

Asked by Topperlearning User 4th June 2014, 1:23 PM

Given: l, m and n are three parallel lines intersected by transversals p and q such that l, m and n cut off equal intercepts AB and BC on p.

To prove: l, m and n cut off equal intercept DE and EF on q also.

Proof: Join AF, suppose it intersect line m at G In ACF, B is the mid-point AC [AB = BC]

And BG||CF

G is the mid-point of AF [Converse of mid point theorem]

In AFD, G is the mid point of AF and GE||AD

E is the mid point of DF

DE = EF

Hence l, m and n cut off equal intercepts DE and EF on q.

Answered by Expert 4th June 2014, 3:23 PM
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