Question

In the given figure MN|| BC and AM: MB= 1: 2

Find area (△AMN)/area (△ABC)

Answer 1

We have 

AM : MB = 1 : 2 

⇒ MB/AM = 2/1 

Adding 1 to both sides, we get

Now, In ∆AMN and ∆ABC 

∠AMN = ∠ABC (corresponding angles in MN || BC) 

∠ANM = ∠ACB (corresponding angles in MN || BC) 

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.