Question

Show that the relation R defined in the set A of all triangles as R = {(T_1, T₂): T1 is similar to T₂}, is equivalence relation. Consider three right angle triangles T₁ with sides 3, 4, 5, T₂ with sides 5, 12, 13 and T₃ with sides 6, 8, 10. Which triangles among T₁, T₂ and T₃ are related?

Answer 1

∴The corresponding sides of triangles T1 and T3 are in the same ratio. Then, triangle T1 is similar to triangle T₃. Hence, T₁ is related to T_3.