Question

See Fig. Show that the triangles whose vertices are Z₁, Z₂,Z₃ and a, b, c (Z₁, Z₂, Z₃ and a, b, c are complex) are similar if |(Z₁,a,1)(Z₂,b,1)(Z₃,c,1)| = 0.

Answer 1

The two triangles are similar if

AB/DE = BC/EF

and ∠ABC = ∠DEF = β (say)

So, Z₁ - Z₂/Z₃ - Z₂ = AB/BC (cosβ + i sinβ)

Similarly, a - b/c - b = DE/EF(cosβ + i sinβ)

Therefore,