Show that the relation R, defined in a set A of all triangles as {(T1, T2) : T1 is similar triangle to T2}, is equivalence relation.

Asked by Topperlearning User | 25th Oct, 2016, 07:54: AM

Expert Answer:

R = {(T1, T2) : T1 is similar triangle to T2}

(i) Any triangle is always similar to itself. So, .
Therefore R is reflexive.
 
(ii) A triangle T1 is similar to T2, then T2 will be similar to T1,
i.e., , then R is symmetric.
 
(iii) If T1 is similar to T2 and T2 is similar to T3, then T1 will also be similar to T3.
So, R is transitive.
 
Since, relation R is reflexive, symmetric and transitive, therefore the R is an equivalence relation.

Answered by  | 25th Oct, 2016, 09:54: AM