Question

The type of the relation "is congruent to" on a set of triangles is .

• A. only symmetric
• B. only transitive
• C. only reflexive
• D. equivalence

Answer 1

The correct option is D equivalence

Any given triangle is congruent to itself. => It is reflexive

If a triangle A is congruent to B, then B will also be congruent to A. This implies if aRb, then bRa, which is the condition for the relation to be symmetric.

If triangle A is congruent to B and B is in turn congruent to C, then we can say A is also congruent to C. From a relation point of view this is same as saying if (a,b) and (b,c) are part of the relation, then (a,c) is also part of the relation, which makes it transitive.

Since the given relation "is congruent to" is reflexive, symmetric and transitive, we can say that it is an equivalence relation.