Let T be the set of all triangles in a Euclid | vedclass

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(D) To determine the nature of the relation $R$ defined by similarity $(a \sim b)$: $1$. Reflexive: Every triangle $a$ is similar to itself $(a \sim a

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An equivalence relation

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(D) To determine the nature of the relation $R$ defined by similarity $(a \sim b)$: $1$. Reflexive: Every triangle $a$ is similar to itself $(a \sim a)$. Thus,$aRa$ holds. So,$R$ is reflexive. $2$. Symmetric: If triangle $a$ is similar to triangle $b$ $(a \sim b)$,then triangle $b$ is also similar to triangle $a$ $(b \sim a)$. Thus,$aRb \implies bRa$. So,$R$ is symmetric. $3$. Transitive: If triangle $a$ is similar to triangle $b$ $(a \sim b)$ and triangle $b$ is similar to triangle $c$ $(b \sim c)$,then triangle $a$ is similar to triangle $c$ $(a \sim c)$. Thus,$aRb$ and $bRc \implies aRc$. So,$R$ is transitive. Since the relation $R$ is reflexive,symmetric,and transitive,it is an equivalence relation.

Let $T$ be the set of all triangles in a Euclidean plane and a relation $R$ on $T$ is defined as $aRb$ if and only if $a \sim b$ (where $a \sim b$ denotes that triangle $a$ is similar to triangle $b$) for all $a, b \in T$. Then $R$ is:

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