Answer:
Given,
AM : MB = 1 : 2
Adding 1 to both sides,
In ∆AMN and ∆ABC
∠???????????? = ∠???????????? (???????????????????????????????????????????????????? ???????????????????????? ???????? ???????? ∥ ????????)
∠???????????? = ∠???????????? (???????????????????????????????????????????????????? ???????????????????????? ???????? ???????? ∥ ????????)
By AA similarity criterion,
∆AMN ~ ∆ ABC
If two triangles are similar, then the ratio of their areas is equal to the ratio of the squares of their corresponding sides.
