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Question 6A (25 marks) (a) Explain what is meant by the converse of a theorem - Leaving Cert Mathematics - Question 6A - 2014
Question 6A
Question 6A (25 marks) (a) Explain what is meant by the converse of a theorem. Explanation: (b) There are some geometric statements that are true, but have conve... show full transcript
Worked Solution & Example Answer:Question 6A (25 marks) (a) Explain what is meant by the converse of a theorem - Leaving Cert Mathematics - Question 6A - 2014
Step 1
Explain what is meant by the converse of a theorem.
Answer
The converse of a theorem is a statement that reverses the roles of the hypothesis and conclusion. For example, in a theorem that asserts, 'If statement A is true, then statement B is true,' the converse would assert, 'If statement B is true, then statement A is true.' It's vital to realize that while the original statement may be true, its converse is not necessarily true.
Step 2
Statement: Give one such geometric statement, and state also the (false) converse.
Answer
Statement: If a shape is a square, then the sides which intersect do so at a 90° angle.
Converse (false): Given a shape, if the sides which intersect do so at a 90° angle, then the shape is a square. This converse is false because other shapes, such as rectangles, also have sides that intersect at 90° angles but are not squares.