Q2 of 23 Page 192

ABCD is quadrilateral E, F, G and H are the midpoints of AB, BC, CD and DA respectively. Prove that EFGH is a parallelogram.


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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9

ABCD is a square. E, F, G and H are the mid points of AB, BC, CD and DA respectively. Such that AE = BF = CG = DH. Prove that EFGH is a square.


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Show that the figure formed by joining the midpoints of sides of a rhombus successively is a rectangle.

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