Answer :

__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 3^{rd} side

__Solution:-__

BD is diagonal of quadrilateral

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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