Question

3.1 Determining SimilarityAre the following triangles similar?If not how do you know

Answer 1

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:

`\measuredangle\alpha\cong\measuredangle\beta`

This means that the triangles have to congruent angles, and by the AA (angle-angle) Theorem, the triangles must be similar.