Math: Proving Similarity

We were asked a question in math: if ∆A is similar to ∆B, and ∆A is similar to ∆ C, is ∆B similar to ∆C?
It is. Here's the proof:
If ∆A is similar to ∆B, that means their corresponding angles are equal, and their corresponding side lengths are proportional by a scale factor. For this matter I'm saying the angles are all 60º, and the side lengths are 2 cm each for ∆A, and the scale factor is 0.5. That means ∆B has 60º angles and 2x0.5=1 cm sides.

Then, ∆A is similar to ∆C. Again, for this matter I'm saying that this scale factor will be 2. That means ∆C has 60º angles and 2x4=8 cm sides.

∆B: 60º angles, 1 cm for each side.
∆C: 60º angles, 4 cm for each side.

They are both equilateral triangles, corresponding angles equal, and corresponding side lengths are proportional by a scale factor of 4. Therefore, they are similar.