Section 1.1 & 1.2: Types of Relations

Show that the relation \(R\) defined in the set \(A\) of all triangles as
\[R = \{(T_1, T_2) : T_1 \text{ is similar to } T_2\}\]
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?