Consider the statement: 'If a quadrilateral is a square, then all four of its sides are equal.' Which of the following is its converse?
Answer and explanation
Correct answer: B. If all four sides of a quadrilateral are equal, then it is a square
- Step 1: Let be 'is a square' and be 'has four equal sides'. The statement is .
- Step 2: The converse swaps the two parts: , 'if the four sides are equal then it is a square'.
Answer
If all four sides of a quadrilateral are equal, then it is a square.
Why not the others: 'If all four sides are equal then it has four right angles' is a different statement about right angles; 'if the four sides are not all equal then it is not a square' is the contrapositive (true, since the original is); 'a square whose sides are not all equal' is the negation of the original; 'a square if and only if its four sides are equal' is the biconditional, a stronger claim than the converse alone. A rhombus shows that the converse itself is false.
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