[Saarang Srini]

ABC ~ A'B'C'

Draw perpendiculars in both triangles at D and D' from A and A' respectively.

ABD ~ A'B'D'

AB/A'B' = AD/A'D' = BD /B'D'

Ar ABC = 1/2 * AC * BD

Ar A'B'C' = 1/2 * A'C' * B'D'

Ar ABC/ Ar A'B'C' = (AC * BD) / (A'C' * B'D') = AC/A'C'  * BD/B'D'

In similar triangles, ratio of all the sides are equal.

Therefore ratio of areAs is equal to AC^2/A'C'^2 = BD^2/B'C'^2 = CA^2/C'A'^2

[Author]

Posts