Prove that a parallelogram is divided into two equal parts by any straight line which passes through the middle point of the diagonal. Share with your friends Share 2 Manbar Singh answered this GIVEN :ABCD is a ∥gm in which BD is one of the diagonal.Suppose the line l bisects the diagonal BD at O.TO PROVE :ar∆ABC = ar∆ADCPROOF :In ∆AOB and ∆COD, we have OB = OD given∠OBA = ∠ODC Alternate interior angles AB = DC Opposite sides of ∥gm are equal⇒∆AOB≅ ∆COD SAS⇒ar∆AOB=ar ∆COD Congruent ∆'s have equal areas ......1In ∆BOC and ∆AOD, we have OB = OD given∠OBC= ∠ODA Alternate interior angles BC = AD Opposite sides of ∥gm are equal⇒∆BOC≅ ∆AOD SAS⇒ar∆BOC=ar ∆AOD Congruent ∆'s have equal areas ......2adding 1 and 2, we getar∆AOB + ar∆BOC=ar ∆COD + ar ∆AOD⇒ar∆ABC = ar∆ADC 0 View Full Answer