You can use the theorems like SSS, SSA to show that they are similar. For example if two triangles have the same 3 sides length or two side lengths equal and 1 angle equal they are similar.
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That is congruent, not similar! Similar is a weaker requirement. All that is needed is that two corresponding angles are the same. Equivalently, the three corresponding sides are in the same proportion.
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They are said to be similar but not congruent triangles.
They are similar triangles.
To prove that two right triangles are similar, all you need to show is that one of them has one acute angle that's equal to one acute angle of the other one.
Two equilateral triangles are always similar!
There are no ratios that can be used for triangles that are not similar.