Question

In a quadrilateral (1)given below,AB||DC,E and F are mid point of AD and BD respectively. prove that
(1) G is mid point of BC
(2) 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=

2

1

(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=

2

1

AB.....(1)

⇒EG∥CD(∵AB∥CD)

Now,

F is the mid-point of BD and FG∥DC

∴G is the mid-point of BC

⇒FG=

2

1

CD.....(2)

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

EF+FG=

2

1

AB+

2

1

DC

⇒EG=

2

1

(AB+CD)

Hence proved.

Answer 2

Answer:

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