Assertion (A): 'Is congruent to' is an equivalence relation on the set of all triangles in a plane.
Reason (R): Congruent triangles have equal areas.

Both A and R are true, and R is the correct explanation of A.Correct answerYour answerBoth A and R are true, but R is not the correct explanation of A.Correct answerYour answerA is true, but R is false.Correct answerYour answerA is false, but R is true.Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

A is true: congruence is reflexive, symmetric and transitive.
R is true, but it is a fact about areas; it does not show that congruence is reflexive, symmetric or transitive.

Worth noting

A true fact about congruent triangles is not, by itself, a reason that congruence is an equivalence relation.

Concept: What an equivalence relation needs
Typical timeTypical: 90 s
Your timeYours: —

The rule this testsEquivalence relations and classes

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Ten questions from Relations & Functions, at your own pace.

Assertion (A): 'Is congruent to' is an equivalence relation on the set of all triangles in a plane.Reason (R): Congruent triangles have equal areas.

Explanation

Assertion (A): 'Is congruent to' is an equivalence relation on the set of all triangles in a plane.
Reason (R): Congruent triangles have equal areas.