### Theory NO. 4 : Determinant and similar triangles

06Feb09

Matrixes seem to have a lot of wonderful properties, for example they may help checking if given triangles represented each by three complex numbers (verticles) are simillar.

So, two triangles represented by complex numbers $\omega_1, \omega_2, \omega_3$ and $z_1, z_2 , z_3$ are similar if, and only if:

$\det{\left[\begin{array}{ccc} \omega_1 & \omega_2 & \omega_3 \\ z_1 & z_2 & z_3 \\ 1 & 1 & 1 \\ \end{array}\right]} = 0$

Proof coming soon.

#### 2 Responses to “Theory NO. 4 : Determinant and similar triangles”

1. 1 tetek

It’s a test message

2. 2 the7new7ramanujan

the proof is easy i guess.
Similarity of triangles arises from same scale transformation and/or a location transformation on the vertices. And in the matrix, [w1 w2 w3] is dependent on [z1 z2 z3] and [1 1 1] iff this happens. Hence proved !! … isn’t it ?