Let AB = a, ad = B, BC = 2B (a > b). Make de ⊥ DC, de intersect AB at point E, connect EC. (1) try to judge whether △ DCE and △ ade, △ DCE and △ BCE are similar. (2) for the above judgment, if the two triangles must be similar, please prove it. (3) if not, please point out when a and B satisfy what relationship, they can be similar?

Let AB = a, ad = B, BC = 2B (a > b). Make de ⊥ DC, de intersect AB at point E, connect EC. (1) try to judge whether △ DCE and △ ade, △ DCE and △ BCE are similar. (2) for the above judgment, if the two triangles must be similar, please prove it. (3) if not, please point out when a and B satisfy what relationship, they can be similar?

These triangles must satisfy certain conditions to become similar triangles, that is, a = √ 3B

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