Are the two triangles similar? How do you know (What Theorem)?

They are similar because of the SAS triangle similarity theorem.

Step-by-step explanation:

The angles in the interconnection of the two triangles are the same because they have the same vertex and lines.

The two sides are similar by a ratio of 1.5.

9/6 and 6/4 both equal to 1.5, which means that they have the same ratio.

Because there is a side that's similar, an angle that's congruent, and then a side that's similar, you can say that the triangles are similar basing on the SIDE-ANGLE-SIDE triangle similarity theorem.