Could we tell whether two matrices are congruent only by its eigenvalues? if not, How many conditions do we need?

Question

When I was learning in my junior high, I am fascinated by the fact that There are more than one way like SSS, SAS etc to tell whether two triangles are congruent or not. Thus I am wondering, Is there a similar criterion for matrices? That is to say, How much conditions is enough to say two matrices is congruent? Is there a theorem of it? If there is, may you tell me the reference? And moreover, Is there a similar theorem for the criterion of similar matrices? Thank you for any advices