Question

6.Prove that the line segments joining
the mid points of the sides of a triangle from four triangles, each of which is similar to the original triangle ​

Answer 1

△ABC in whichD, E, F are the mid points of sides AB, BC and CA respectively.

To prove:- each of the triangles are similar to the original triangle, i.e.,

△ADF∼△ABC

△BDE∼△ABC

△CEF∼△ABC

Proof:-

Consider the △ADF and △ABC

Since D and F are the mid points of AB and AC respectively.