Question

ABCD is a quadrilateral with unequal sides, unequal diagonals and unequal angles. E, F, G, H are the middle points of the four sides, then EFGH is a:

• A. quadrilateral with unequal sides
• B. parallelogram
• C. rhombus
• D. rectangle

Answer 1

Answer: (B)

parallelogram

ABCD is a quadrilateral with unequal sides. E, F, G, H are the midpoints of four sides. Join the diagonals of the quadrilateral: BD and AC.
Now, in the triangle ABD (refer to the figure), H and E are the midpoints of the sides AD and AB respectively. Hence HE || BD. Similarly in the triangle BCD, FG || BD. So, we get HE || GF.
Similarly, by considering the triangles ABC and ACD, we get EF || AC, and GH || CA.
So, we get that for the quadrilateral EFGH, opposite sides are parallel. That makes it a parallelogram.