Question

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

(see Fig. 8.28). Show that l, m and n cut off equal

intercepts DE and EF on q also.

Answer 1

Given:(1)l||m||n
(2)AC=BC
=B is the mid point of AC
To prove=DE=EF
E is the mid point of DF

proof: in ∆ACF
since,m||n
hence, BG||CF
& B is the mid point of AC
by converse ofmid point theorem
G is the mid point of AF
know in ∆AFD
GE||AD.....(m||l)
& G is the mid point of AF (proved above)
so from converse of mid point theorem
E is the mid point of DF
_
_DE=DF
Hope you understand...:))