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Show that the relation R defined in the ...

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.

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To 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 an equivalence relation, we need to verify that it satisfies three properties: reflexivity, symmetry, and transitivity. ### Step 1: Check Reflexivity A relation is reflexive if every element is related to itself. For our relation, this means that for any triangle \( T_1 \), it must be similar to itself. **Proof:** - Any triangle \( T_1 \) is similar to itself because it has the same angles and proportions. - Therefore, \( (T_1, T_1) \in R \) for all triangles \( T_1 \). ...
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