Why do we have to subtract BODE from both sides in example 3 ?

 

Hi Medha!

Hope, you have clearly understood to the following line of the solution of the stated example.

area (ABEF) = area (ABCD)    … (ii)

 

You are required to prove, area (BODE) = area (AOD) + area (BEC)

 

According to the given figure; area (AOD) + area (BEC) is equal to area (ABCD) – area (BODE).

 

In order to obtain area (AOD) + area (BEC) in the R.H.S. of the proof, it is required to subtract area (BODE) from both sides of the equation (ii).

∴ area (ABEF) – area (BODE) = area (ABCD) – area (BODE)

⇒ area (AODF) = area (AOD) + area (BEC)  … (iii)

 

You have already a relationship (i) as:

area (AODF) = area (BODE)  … (i)

 

From (i) and (iii),

area (BODE) = area (AOD) + area (BEC)

 

Hope! This helps you.

 

Cheers!