In the similar triangles II problem, I dont understand why if both triangles share the same height y, how their bases can then be proportional. I thought base and height had to be proportional? how can we infer the base of the smaller triangle is y/2 because the base of the larger triangle is 2y and they share the height y?

Give more context (which question? share a screenshot).

I think by this way we can prove the two triangles are similar due to Angle-Angle-Angle Similarity