Question

In a adjoining figure D,E,Fare the midpoints of the sides BC,CA and AB respectively ,of triangle ABC show that angle EDF

Answer 1

Given: In ΔABC, D,E and F are midpoints of sides AB,BC and CA respectively.

BC=EC

Recall that the line joining the midpoints of two sides of a triangle is parallel to third side and half of it.

Therefore,we have:

From (1), (2) and (3) we have

But if in two triangles, sides of one triangle are proportional to the sides of the other triangle, then their corresponding angles are equal and hence the two triangles are similar

Therefore, ΔABC∼ΔEDF [By SSS similarity theorem]

Hence area of ΔABC: area of ΔDEF=4:1