Q. 24.1( 16 Votes )

ABCD is quadrilat

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 3rd 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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