you know what all these terms mean right? just go through the check list with each part.

example, for the first.

Test reflexive:a. The congruence relation on the set of triangles.

is it true that every triangle is congruent to itself? YES. Therefore this relation is reflexive

Test symmetric:

is it true that if triangle A is congruent to triangle B, then triangle B is congruent to triangle A (for all triangles A and B)? YES. Thus, this relation is symmetric.

Test transitive:

is it true that if triangle A is congruent to triangle B and triangle B is congruent to triangle C, then triangle A will be congruent to triangle C? YES. So the relation is transitive.

Test Irreflexive:

We already know the relation is reflexive, so it cannot be irreflexive.

You could also note (from previous knowledge) that congruence is an equivalence relation, so we know right off the bat it is reflexive, symmetric and transitive. And so cannot be irreflexive.

Try the others in the same way