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 = Money2

Money is the root of all evil.Money = Evil

By substitution: Girls = ( Evil )2

Therefore: Girls = Evil