Anya Wants To Prepare Poster On Education Of Girlchild For Campaign

Anya wants to prepare a poster on education of girlchild for a campaign. She takes a triangular … the development of a society?…

Answers:

Given: A △ABC in which medians AD, BE and CF intersect at G.

To prove: ar (△AGB) = ar (△BGC) = ar (△CGA)  = 1/3 ar (△ABC)

Proof: In △ABC, AD is the median. As a median of a triangle divides it into two triangles of equal area. 

∴  ar (△ABD) = ar (△ACD)           ….(i)

In △GBC, GD is the median

∴ ar (△GBD) = ar (△GCD)   …..(ii) 

Subtracting (ii) from (i), we get 

ar (△ABD) – ar (△GBD) = ar (△ACD) – ar (△GCD)

ar (△AGB) = ar (△AGC)      …..(iii)

Similarly, ar (△AGB) = ar (△BGC)    …..(iv)

From (iii) and (iv), we get

ar (△AGB) = ar (△BGC) = ar (△AGC)     …(v)

But,  ar (△AGB) + ar (△BGC) + ar (△AGC) = ar (△ABC)   ….(vi)

From (v) and (vi), we get

3 ar (△AGB) = ar (△ABC) 

⇒ ar (△AGB) = 1/3 ar (△ABC)

Hence,  ar (△AGB) = ar (△AGC) = ar (△BGC) = 1/3 ar (△ABC)

Yes, for the development of a society, education of each girl child is essential. An educated society always progresses.