Given:- ABCD is quadrilateral E, F, G and H are the midpoints of

AB, BC, CD and DA respectively

Formula used:- Line joining midpoints of 2 sides of triangle

Is parallel to 3rd side

Solution:-

EH is the line joined by midpoints of triangle ABD,

EH is parallel to BD

GF is line joined by midpoints of side BC&BD of triangle BCD

GF is parallel to BD

If HE is parallel to BD and BD is parallel to GF

It gives HE is parallel to GF

AC is another diagonal of quadrilateral

GH is the line joined by midpoints of triangle ADC,

GH is parallel to AC

FE is line joined by midpoints of side BC&AB of triangle ABC

FE is parallel to AC

If GH is parallel to AC and AC is parallel to FE

It gives GH is parallel to FE

As HE||GF and GH||FE

EFGH is a parallelogram

Conclusion:-

EFGH is a parallelogram

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