Show that the relation ‘is congruent to’ on the set of all triangles in a plane is an equivalence relation

What is an equivalence relation? Show that the relation of'similarity' on the set S of all triangle in a plane is an equivalence relation.

Show that the relation "is parallel to" on the set S of all straight lines in a plane is an equivalence relation.

Prove that the relation congruence modulo m on the set Z of all integers is an equivalence relation.

Show that the relation R defined on the set A of all triangles in a plane as R={(T_1,\ T_2): T_1 is similar to T_2) is an equivalence relation. Consider three right angle triangle T_1 with sides 3,\ 4,\ 5; T_2 with sides 5,\ 12 ,\ 13 and T_3 with sides 6, 8, 10. Which triangles among T_1,\ T_2 and T_3 are related?

Which one of the following relations on R is an equivalence relation?

Show that the relation R on the set A{xZ ;0lt=12}, given by R={(a , b): a=b}, is an equivalence relation. Find the set of all elements related to 1.

The relation ''is a factor of'' on the set N of all natural number is not

Show that the relation R on the set Z of integers, given by R={(a ,\ b):2 divides a-b} , is an equivalence relation.

Show that the relation R on the set Z of integers, given by R={(a ,\ b):2 divides a-b} , is an equivalence relation.

Which of one of the following relations on R is equivalence relation