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smc

prealgebra intermediate

Problem

Given the true statement: If a quadrilateral is a square, then it is a rectangle. It follows that, of the converse and the inverse of this true statement is:
(A)
(B)
(C)
(D)
Solution
First, let us list the statement "If a quadrilateral is a square, then it is a rectangle" as a statement of the form "If , then ". In this case, is "a quadrilateral is a square", and is "it is a rectangle". The converse is then: "If , then ". Plugging in, we get "If a quadrilateral is a rectangle, then it is a square". However, this is obviously false, as a rectangle does not have to have four sides of the same measure. The inverse is then: "If not , then not ". Plugging in, we get "If a quadrilateral is not a square, then it is not a rectangle". This is also false, since a quadrilateral can be a rectangle but not be a square. Therefore, the answer is .
Final answer
D