1959 AHSME Problems/Problem 6
Problem 6
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:
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 .
See also
1959 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 5 |
Followed by Problem 7 | |
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