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.

Explanation

To show that the relation \( R \) defined on the set \( T \) of all triangles is an equivalence relation, we need to demonstrate that it satisfies three properties: reflexivity, symmetry, and transitivity.

### Step 1: Reflexivity
A relation \( R \) is reflexive if every element is related to itself.

For any triangle \( T_1 \) in the set \( T \):
- A triangle is congruent to itself, which means \( T_1 \cong T_1 \).
- Therefore, we can say that \( (T_1, T_1) \in R \).
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