Question

if three or more parallel lines make equal intercepts on a given transversal then prove that they will make equal intercepts on any other transversal also.

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Answer 1

Answer:

Let l,m,n are three paralle lines intersected by transversals p and q suvh that l,m and n cutt off equal intercept AB and BC on p.

we have to prove l,m and n cut off equal intercept DE and EF on q also.

Proof : Join AF, Suppose it intersects line m at G

In △ACF,B is midpoint of AC because (AB=BC)

and BG is parallel to CF

∴ G is mid point of AF by converse of midpoint theorem

In △AFD,G is mid point of AF and GE∥AD

∵E is midpoint of DF

⇒DE=EF

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