Usha drew a quadrilateral EFGH in such a way that EF = EH and GF = GH

 Usha drew a quadrilateral EFGH in such a way that EF = EH and GF = GH.

Which of these is DEFINITELY true about its diagonals EG and FH?
1 they are equal in length
2 they bisect each other
3 they are perpendicular to each other
4 (We cannot say any of these.)

Given:  is a quadrilateral.

Points  are the midpoints of  and 

Draw diagonals  and  in the quadrilateral 

Segment  is the midpoint segment in 

 segment  is parallel to the side  of the 
     (Line segment joining midpoints of two sides of a triangle property.)

Similarly, Segment  is the midpoint segment in 

 Segments  is parallel to side  of 

Since, Segment  and  are both parallel to the diagonal , they are parallel to each other.

Segment  is the midpoint segment in 

 Segment  is parallel to side  of 

Segment  is midpoint segment in 

 Segment  is parallel to side  of triangle 

Since,Segment  and  are both parallel to diagonal , they are parallel to each other.

Thus, we have proved that in quadrilateral  the opposite sides 
 and , and  are parallel by pairs.

Hence, the quadrilateral  is the parallelogram.
So, The answer is they both bisect each other

solution

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