Question

if E F G and H are respectively the midpoints of the sides of a parallelogram ABCD show that area of efgh equal half area of ABCD

Answer 1

Given: ABCD a parallelogram in which          E,F,G,H, are mid points of AB,BC,CD,AD. 
Then to prove: ar(EFGH) = ar(ABCD) 
Construction: Draw HF parallel to AB and CD. 
Proof:  AB is parallel and equal to HF .

Therefore, ABFH is a parallelogram Since, triangle EFH and parallelogram ABFH lies on the same base HF and between same parallels AB and HF.  

Therefore, ar(EFH) = 1/2 ar (ABFH)   -(1)                        
 Now, DC is parallel and equal to HF. Therefore,DCFH is a parallelogram Since, triangle GFH and parallelogram DCFH lies on the same base HF and between same parallels DC and HF. 

Therefore, ar(GFH) = 1/2 ar (DCFH)   -(2)                         
From 1 and 2 we get,               

ar(EFH) + ar (GFH) = 1/2 ar (ABFH) + 1/2 ar (DCFH)
ar (EFGH) = 1/2 ( ar(ABFH) + ar(DCFH))               ar (EFGH) = 1/2 ( ar(ABCD)) ar (EFGH)
at (EFGH) = 1/2 ar (ABCD)                    

  proved


HOPE THIS WILL HELP...

Answer 2

Answer:here is the ans it aay help you

Step-by-step explanation: