The following is a conditional statement: If I go to the mall, then I use my credit card. If I use my credit card, I must be at the mall. What do you think the hypothesis is? What do you think the conclusion is? What do you think the converse is? Is the converse true?

Conditional Statement: Hypothesis: Conclusion: Converse: a statement in the if-then form tells if one thing happens, another will follow what you are assuming to be true in order to prove the conclusion part of the statement followed by the hypothesis Swapping the conditional, so IF conclusion, THEN hypothesis.

A heavy object stored in the attic of a jungle mansion may crash down on the occupants. A line that bisects an angle in a triangle bisects the opposite side. If a heavy object is stored in the attic of a jungle mansion, then it may crash down on the occupants. If a line bisects an angle in a triangle, then it bisects the opposite side.

Lewis Carroll, the author of Alice’s Adventures in Wonderland and Through the Looking Glass, was a mathematics teacher who wrote stories as a hobby. His books contain many amusing examples of both good and deliberately poor logic and, as a result, have long been favorites among mathematicians. Consider the following conversation held at the Mad Hatter’s Tea Party: “Then you should say what you mean,” the March Hare went on. “I do,” Alice hastily replied; “at least – at least I mean what I say – that’s the same thing, you know.” “Not the same thing a bit!” said the Hatter. “Why, you might just as well say that ‘I see what I eat’ is the same thing as ‘I eat what I see’!” “You might just as well say,” added the Doormouse, who seemed to be talking in his sleep, “that ‘I breathe when I sleep’ is the same thing as ‘I sleep when I breathe’!” “It is the same thing with you,” said the Hatter, and here the conversation dropped, and the party sat still for a minute. Carroll is playing here with pairs of related statement, and the Hatter, Hare, and the Doormouse are right: these sentences in each pair do not say the same thing at all. Consider the Doormouse’s example. If we change his two statements into “if-then” form, we get

 Identify in the statement and converse the hypothesis and conclusion. Statement: If I sleep, then I breathe. Converse: If I breathe, then I sleep. Although both statements may be true of the Doormouse, the first statement is true and the second statement is false for ordinary beings.

Example: The following statement is true: If you are a U.S. Astronaut, you are not more than six feet tall. Write the converse. Is it true? If a conditional statement is true, can the: converse be false? 1.If a point is a midpoint, then it divides the segment into two congruent segments. Converse: If a point divides the segment into two congruent segments, then it’s a midpoint.

For the following write the conditional statement and the converse. Determine if the statements are true or false. 3. Equilateral triangles are equiangular. 4. Equilateral quadrilaterals are equiangular. 5. A triangle with two congruent angles is isosceles. If a triangle is equilateral, then the triangle is equiangular. If a triangle is equiangular, then the triangle is equilateral.

6. All right angles are congruent. 7. Parallel lines form congruent alternate interior angles.

 Homework: Come up with 5 conditional statements

“Proof” That Girls Are Evil Girls require time and money. Girls = Time Money Time is money. Time = Money Therefore:Girls = Money Money = Money 2 Money is the root of all evil.Money = Evil By substitution:Girls = ( Evil ) 2 Therefore:Girls = Evil