In ΔABC, D and E are the midpoints of AB and AC respectively. Find the ratio of the areas of ΔADE and ΔABC.

Question

Philoid · Accepted Answer

In ΔABC and ΔADE

It is given that AD = DB and AE = EC

Also ∠ A = ∠ A

So, by SAS similarity criterion ΔADE ~ ΔABC

We know that if two triangles are similar then the ratio of their areas is equal to the ratio of the squares of their corresponding sides.