Question

abcd is a trapezium in which ab||dc and e is the midpoint of ad. f is the midpoint of bc such that ef||ab. prove that (i) f is the midpoint of bc (ii)ef = 1/2(ab+dc)​

Answer 1

Answer:Figure shows the trapezium ABCD.

 

AB || CD  (given)

 

E is mid point of AD (given)

 

EF || DC (given)

 

Let us join BD and let EF meets BD at G.

 

since EF || DC and AB || DC, we have EG || AB.

 

In Δ ABD, EG || AB and E is mid point of AD. Hence EG = (1/2)AB and BG = DG ................(1)

 

similarly we can say GF || DC.

 

in Δ BCD,  FG || CD and G is mid point of BD. Hence GF = (1/2)DC ..........................(2)

Step-by-step explanation: