Q5 of 180 Page 1

The line segment joining the midpoints of the adjacent sides of a quadrilateral form a ________ .

Consider the below diagram.



ADCB is the quadrilateral. E, F, G, H are the midpoints of the corresponding sides. Join EF, FG, GH, HE, FH, EG and AC.


Midpoint theorem states that in a triangle, the line segment joining the mid points of any two sides of a triangle is parallel to the third side and is half of the third side.


Using midpoint theorem, In triangle BAC


⇒ EF || AC, EF = AC


Using midpoint theorem, In triangle ACD


⇒ HG || AC, HG = AC


From these two equations, we conclude that


⇒ EF || HG and EF = HG


∴ EFGH is a parallelogram.


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