The following is a conditional statement: If it is Saturday, then I do not go to school. 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: a statement with two parts: an “if” part and a “then” part Hypothesis: the “if” part of an if-then statement Conclusion: the “then” part of an if-then statement Converse: the statement formed by switching the hypothesis and conclusion

Write in conditional form: All leap years have 366 days. If it is a leap year, then it has 366 days. Two lines that are perpendicular to the same line are parallel to each other. If two lines are perpendicular to the same line, then they are parallel.

A heavy object stored in the attic of a jungle mansion may crash down on the occupants. If a heavy object is stored in the attic of a jungle mansion, then it may crash down on the occupants. A line that bisects an angle in a triangle bisects the opposite side. If a line bisects and 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. Hypothesis: if I sleep Conclusion: then I breathe Hypothesis: If I breathe Conclusion: then I sleep

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 you are not more than six feet tall, then you are a U.S. Astronaut. (false)

For the following write the conditional statement and the converse. Determine if the statements are true or false. 1.At least two medians of an equilateral triangle are congruent. 2.Equilateral triangles are equiangular. 3. Equilateral quadrilaterals are equiangular. 4. A triangle with two congruent angles is isosceles. 5. All right angles are congruent. 6. Parallel lines form congruent alternate interior angles.

 Homework: Finish Worksheet AND Enjoy the Weekend!!!!