Answer :

(i) ΔAYC and Δ BCY are on the same base CY and between the same parallels

CY || AB


Area (ΔAYC) = Area (ΔBCY)


(Triangles on the same base and between the same parallels are equal in area)


Subtracting ΔCXY from both sides we get,


Area (ΔAYC) – Area (ΔCXY) = Area (ΔBCY) – Area (ΔCXY) (Equals subtracted from equals are equals)


Area (ΔCBX) = Area (ΔAXY)


(ii) Since, ΔACC and ΔADE are on the same base AF and between the same parallels


CD || AF


Then,


Area ( = Area ()


Area () + Area ( = Area () + Area (


Area ( = Area () (i)


(iii) Since, ΔCBY and ΔCAY are on the same base CY and between the same parallels


CY || BA


Then,


Area () = Area ()


Adding Area ( on both sides we get


Area ( + Area ( = Area ( + Area ()


Area ( = Area ( (ii)


Compare (i) and (ii), we get


Area ( = Area (


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