Let `T` be the set of all triangles in the Euclidean plane, and let a relation `R` on `T` be defined as `a\ R\ b` if `a` is congruent to `b` for all `a ,\ b in T` . Then, `R` is (a) reflexive but not symmetric (b) transitive but not symmetric (c) equivalence (d) none of these

Explanation

Let there be three triangles a,b,c in Euclidean plane such that `aRb` and `bRc`.

We know that if triangle a is congruent to triangle b and triangle `b` is congruent to
triangle `c`, triangle a must also be congruent to triangle c .

So, `aRc` and thus relation R is transitive .


Also we know that any triangle in Euclidean plane is always congruent to itself
.
So, `tRt` and thus relation R is reflexive .


Let there be two triangles n and m in Euclidean plane.

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