We want to know if the triangles shown are similar or not.
We affirm that the blue angle shown is the same for both triangles, and thus, the triangles have a congruent angle.
Now, the following orange lines are parallel, and the blue line is a transversal of both lines.
This means that the corresponding angles are congruent:
Which is that:
[tex]\measuredangle\alpha\cong\measuredangle\beta[/tex]
This means that the triangles have to congruent angles, and by the AA (angle-angle) Theorem, the triangles must be similar.
