CBSE Class 9 Answered

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.