Assume that the delta ABC A B1 C1 similar where the corners

Assume that the delta ABC ~ A B_1 C_1 (similar), where the corners A, B, C and respective A, B_1, C_1 in both triangles are marked in the same order, both in the anticlock wise direction. Show that the interaction M notequalto A between these two triangles concides with the interaction of lines B B_1 and C C_1.

Solution

For the question it is enough to show that the sides are concurrent for the similar triangles

As it is given that the triangles are similar,

AB/A₁B_{1 =} BC/B₁C₁= CA/C₁A₁= r

Let M be the intersection of AA₁ and BB_1.

As A₁B_{1 ||} AB , triangle MAB is similar to triangle MA₁B₁ with scale factor r