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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 G is mid point of BC.
1458348_ac597d4420c24aba98676285ed32d4d8.png

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Solution

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

To prove:- G is the mid-point of BC

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

Hence proved.

1364648_1458348_ans_46fd53b498604559bcc32e3a2e3d552d.png

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