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.
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]
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.
You have rated this answer /10