Let T be the set of all triangles in a plane with R a relation in T given by : `R = {(T_1, T_2) : T_1` is congruent to T_2}. Show that R is an equivalence relation.

Let L be the set of all lines in XY plane and R be the relation in L defined as R= {(L_1 ,L_2): L_1 is parallel to L_2 )}. Show that R is an equivalence relation. Find the set of all lines related to the line y = 2x + 4.

Let L be the set of all lines in XY-pJane and R be the relation in L defined as R={(L_(1), L_(2)): L_(1) is parallel to L_2 }. Show that R is an equivalence relation. Find the set of all lines related to the line y = 2x + 4

Let L be the set of all lines in XY plane and R be the relation in L defined as R={(L_(1),L_(2)),L_(1) is parallel to L_(2)} . Show that R is an equilavence relation.

Show that relation R = {(T_1, T_2) : T_1 is similar to T_2 }, defined on the set of all triangles, is an equivalence relation.

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

Show that the relation R defined in the set A of all triangles as : R = [(T_1, T_2): T_1 and T_2 are similar triangles} is an equivalence relation .

Show that the relation R defined in the set A of all triangles as R={(T_(1),T_(2)):T_(1) is similar to T_(2)} is an equivalence relation.

Show that the relation R, defined by the set A of all triangles as : R = { (T_1, T_2) = T_1 is similar to T_2} is an equivalence relation. Consider three right-angled triangles T_1 with sides 3, 4, 5, T_2 with sides 5, 12, 1 3 and T_3 with sides 6, 8, 10.