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Question

In the quadrilateral (1) given below, AB||DC, E and F are mid point of AD and BD respectively. Prove that
EG=12(AB+DC)
1458357_d2629ce4a71d47348752d2a5a2f3e758.png

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Solution

Given:- ABDC,E and F are mid-points of AD and BD respectively.

To prove:- EG=12(AB+DC)

Proof:-

In ABD,

DF=BF(F is the mid-point of BD)

Also, E is the mid-point of AD(Given)

Therefore,

EFAB and EF=12AB.....(1)

EGCD(ABCD)
Now,

F is the mid-point of BD and FGDC

G is the mid-point of BC

FG=12CD.....(2)

Adding equation (1)&(2), we have

EF+FG=12AB+12DC

EG=12(AB+CD)

Hence proved.

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