In ∆ABC, D and E are the midpoints of AB and AC respectively. Find the ratio of the areas of ∆ADE and ∆ABC.

 

 

 

 

Answer:

Given,

D and E are midpoints of AB and AC.

Applying midpoint theorem,

DE ‖ BC.

By B.P.T.,

∠???? = ∠????

Applying SAS similarity theorem,

∆ ADE~ ∆ ABC.

The ratio of areas of these triangles will be equal to the ratio of squares of their corresponding sides.