Question

In quadrilateral ABCD, AB | CD, E and F are midpoints of AD and BD
respectively. G is any point on BC and (E-F-G). Prove that
i) G is the midpoint of BC
ii) EG = 1/2(AB + CD)
.
please show all steps​

Answer 1

Answer:

Given: AB||CD, E & F are mid points of AD & BD

Step-by-step explanation:

Proof: (i) In ∆ABD,

DF=BF ( F is midpoint of BD),

Also, E is midpoint of AD (Given)

So, EF||AB & EF = 1/2 AB (eq 1)

EG||CD [As AB||CD]

Now, F is the midpoint of BD & FG||DC

Therefore, G is midpoint of BC

(ii) FG=1/2 CD (eq 2)

adding equation 1 & 2 , we have

EF+FG = 1/2 AB + 1/2 CD

EG = 1/2( AB+CD)

Hence proved