Answer :

(i) In , we have

MB = AB


BC = BD


And,


MBC = ABD (Therefore, MBC and ABC are obtained by adding ABC to right angle)


So, by SAS congruence rule, we have



Area () = Area ( (1)


(ii) Clearly, and rectangle BYXD are on the same base BD and between the same parallels AX and BD


Therefore,


Area ( = Area of rectangle BYXD


Area of rectangle BYXD = 2 Area ()


Area of rectangle BYXD = 2 Area () (2)


[Therefore, Area ( = Area (] From (1)


(iii) Since,


and square MBAN are on the same base MB and between the same parallel MB and NC


Therefore,


2 Area () = Area of square MBAN (3)


From (2) and (3), we have


Area of square MBAN = Area of rectangle BXYD


(iv) In , we have


FC = AC


CB = CE


And,


FCB = ACE (Therefore, FCB and ACE are obtained by adding ACB to a right angle)


So, by SAS congruence rule, we have



(v) We have,



Area ( Area (


Clearly,


and rectangle CYXE are on the same base CE and between the same parallel CE and AX


Therefore,


2 Area ( = Area of rectangle CYXE


2 Area ( = Area of rectangle CYXE (4)


(vi) Clearly,


and rectangle FCAG are on the same base FC and between the same parallels FC and BG


Therefore,


2 Area ( = Area of rectangle FCAG (5)


From (4) and (5), we get


Area of rectangle CYXE = Area of rectangle ACFG


(vii) Applying Pythagoras theorem in , we have


BC2 = AB2 + AC2


BC * BD = AB * MB + AC * FC


Area of rectangle BCED = Area of rectangle ABMN + Area of rectangle ACFG


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