Question

If E, F, G and H are respectively the midpoints of the sides AB, BC, CD and AD of a parallelogram ABCD, show that ar (EFGH) = 1/2 ar (ABCD).

Answer 1

Given that □ABCD is a parallelogram. 

E, F, G and H are the midpoints of the sides. Join E, G. 

Now ΔEFG and □EBCG he on the same base EG and between the same parallels

EG // BC. ∴ ΔEFG = 1/2 □EBCG ……………(1)

Similarly, 

ΔEHG = 1/2 □EGDA …………….(2)

Adding (1) and (2);

ΔEFG + ΔEHG = 1/2 □EBCG + 1/2 □EGDA

□EFGH = 1/2 [□EBCG +□ EGDA]

□EFGH = 1/2 [□ABCD]

Hence proved.