the corresponding sides are congruent
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Yes.
no
90 degree triangles are always similar.
All equiangular triangles are similar, but not congruent. They all have three 60 degree angles. This does not mean that they all have the same side lengths though. Therefore, they are only similar, not congruent.
If one corner is right, the other corners are together 90 degrees. So they're both still variable. So: no not all right triangles are similar