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.

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 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 equivalence relation. Consider three right angle triangles 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 ?

Show that the relation R defined in the set A of all polygons as R = {(P _(1), P _(2)): P _(1) and P _(2) have same number of sides}, is an equivalence relation. What is the set of all elements in A related to the right angle triangle T with sides 3,4 and 5 ?

R_1 and R_2 are two equivalence relation defined on set A(ne phi) . Show that R_1capR_2 is an equivalence relation.

If R _(1) and R _(2) are equivalence rrelations in a set A show that R _(1) nn R _(2) is also an equivalence relation.

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

Show that the relation R defined on the set A of a polygons as R = {P_(1),P_(2) : P_(1) "and " P_(2) have same number of sides } is an equivalence relation. What is the set of all elements in A related to the right angle triangle T with sides 3,4 and 5 ?

Let p , q , r be the altiudes of triangles with area s and perimeter 2 t . Then the value of (1)/(p)+(1)/(q)+(1)/(r) is _