Q. 33.9( 15 Votes )

Show that the fig

Answer :


Given:- ABCD is a rhombus


E,F,G,H are the mid points of AB,BC,CD,DA


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


Is parallel and half of 3rd side


Solution:-


BD is diagonal of rhombus


EH is the line joined by midpoints of triangle ABD,


EH is parallel and half of BD


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


GF is parallel and half BD


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


It gives HE is parallel to GF


If HE is half of BD and GF is also half of BD


It gives HE is equal to GF


AC is another diagonal of rhombus


GH is the line joined by midpoints of triangle ADC,


GH is parallel to AC


GH is half of AC


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


FE is parallel to AC


FE is half of AC


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


It gives GH is parallel to FE


If GH is half of AC and FE is also half of AC


It gives GH is equal to FE


As diagonals of rhombus intersect at 90°


And AC is parallel to FE and GH


All angles of EFGH is 90°


All angles are 90° and opposite sides are equal and parallel


Conclusion:-


EFGH is a rectangle


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