Question

In a figute abcd is trapezium in which abll dc .Bd is a diagonal and e is the mid- point of ad .A line is draw throught e parallel to ab , intersecting bcat f .Show that f is the mid point of bc.

Answer 1

In tri.ADC
E is the mid-point of AD.
EG//AB.
G is the mid-point of DC.(convers of mid-point theorem)

In tri.ABC
G is the mid-point of BD.
GF//CD
F is also the mid-point of BC.

Answer 2

Let EF intersect DB at G.

By converse of mid-point theorem, we know that a line drawn through the mid-point of any side of a triangle and parallel to another side, bisects the third side.

In ΔΑBD ,

EF || AB and E is the mid-point of AD.

Therefore, G will be the mid-point of DB. As EF || AB and AB || CD,

: EF || CD (Two lines parallel to the same line are parallel to each other)

In ∆BCD, GF || CD and G is the mid-point of line BD. Therefore, by using converse of mid-point theorem,F Is the mid-point of BC.