Which one of these pairs of triangles need NOT be similar?

Two pairs of equal angles is the AA criterion, so those triangles are similar. Every equilateral triangle is 60°–60°–60°, and a right triangle containing 45° is forced to be 90°–45°–45°, so both of those pairs are similar. But an isosceles triangle containing a 70° angle may be 70°–70°–40°, with 70° as a base angle, or 70°–55°–55°, with 70° as the apex — and those two are not similar. The trap is assuming that one stated angle plus the word isosceles pins the shape down; it does not, because the angle can sit in two different places.