Question

ii) In the quadilatural given below , AB //DC,E
and F mid-points of AD and BD
respectively .
A
Prove that:
a) G is the mid-point of BC
b) EG= 1/2(AB+DC)​

Answer 1

Answer:

Given:- AB∥DC,E and F are mid-points of AD and BD respectively.

To prove:- EG=21(AB+DC)

Proof:-

In △ABD,

DF=BF(∵F is the mid-point of BD)

Also, E is the mid-point of AD(Given)

Therefore,

EF∥AB and EF=21AB.....(1)

⇒EG∥CD(∵AB∥CD)

Now,

F is the mid-point of BD and FG∥DC

∴G is the mid-point of BC

⇒FG=21CD.....(2)

Adding equation (1)&(2), we have

EF+FG=21AB+21DC

⇒EG=21(AB+CD)