Question

ABCD is a trapezium in which AB is parallel to DC, bd is a diagonal and E is the mid point of AD a line is drawn through E parallel to AB intersecting BC at F show that F is the mid point of BC​

Answer 1

F is the mid point of BC. (Proved)

Explanation:

See the attached diagram.

Given AB ║ CD and EF is drawn to be parallel to AB.

So, EF ║ AB ║ CD .......... (1)

Now, in Δ ABD, E is the midpoint of AD and EG is parallel to AB.

So, G must be the midpoint of BD.

Now, in Δ BCD, G is the midpoint of DB and GF is parallel to CD. {From relation (1)}

So, we can write F is the midpoint of BC. (Proved)

[Since we know the theorem that if we joint the midpoints of two sides of a triangle then the line formed will be parallel to the third side.]