Prove that triangle abc must be isosceles

First let us determine what <ABD is: 180º- 90º - 2nº = 90-2nº (the square represents a 90º angle

Then find <DCB: 180º - 90º - nº = 90-nº

Angle <ACB doesn't change: it is 90-n

but, <ABD is only part of <ABC: if we add <ABD with <DBC then we get 90-2n+n = 90-n

Definition of an isoceles triangle: It has two sides that are congruent or has two angles that are congruent.

Because both <ABC and <ACB equal 90-n the triangle ABC is an isoceles triangle.

Hope this Helps, and May the Force Be With You!

-Jabba