Students will analyze statements, write definitions as conditional statements and verify validity. Why? So you can verify statements, as seen in Ex 2. Mastery is 80% or better on 5-min checks and indy work. “If I get straight A’s, then my parents will buy me a car”

Key Vocabulary Conditional Statement- page 79 If-then form – If Hypoth, then conclusion Hypothesis- page 79 Conclusion- page 79 Negation- Opposite of original statement. Converse- If C then H Inverse – If not H then not C Contrapositive- If not C then not H Equivalent statements- Both true or both false Perpendicular lines- two line intersect at a right angle Biconditional statement- If and only if…when conditional and converse are true statements

In mathematics, you will come across many _______________. For Example : If a number is even, then it is divisible by two. If – then statements join two statements based on a condition: A number is divisible by two only if the number is even. Therefore, if – then statements are also called ________ _______. if-then statements conditional statements

Conditional statements have two parts. The part following if is the _________. hypothesis The part following then is the _________. conclusion If a number is even, then the number is divisible by two. a number is even the number is divisible by two. Hypothesis: Conclusion:

Pair Share: Guided What about? If__________________________, then_________________________ If it is a vertebrate, then it has a backbone. If X equals 2, then X² equals 4

How do you determine whether a conditional statement is true or false? Conditional Statement True or False Why? If it is the 4 th of July (in the U.S.), then it is a holiday. True The statement is true because the conclusion follows from the hypothesis. If an animal lives in the water, then it is a fish. False You can show that the statement is false by giving A counter example one counterexample Whales live in water, but whales are mammals, not fish.

In your notes determine whether each conditional statement is true or false? Conditional Statement True or False Why? If you were on the BCHS varsity football team last year, then you were a league champion. If Kobe Bryant scores 40+ points, then the Lakers win. True False The statement is true because the conclusion follows from the hypothesis. You can show that the statement is false by giving one counterexample. Kobe could score 40+ and the Lakers could lose.

The ________ of a conditional statement is formed by exchanging the hypothesis and the conclusion. converse Conditional: If a figure is a triangle, then it has three angles. a figure is a triangle it has three angles Converse: If _______________, then _________. NOTE: You often have to change the wording slightly so that the converse reads smoothly. Converse: If the figure has three angles, then it is a triangle.

To write a Converse Switch the hypothesis & conclusion parts of a conditional statement. Ex: Write the converse of “If you are a brunette, then you have brown hair.” If you have brown hair, then you are a brunette. CONVERSE

Negate the hypothesis & conclusion of a conditional statement. Ex: Write the inverse of “If you are a brunette, then you have brown hair.” If you are not a brunette, then you do not have brown h air. To write an Inverse Skill Develop

Negate, then switch the hypothesis & conclusion of a conditional statement. Ex: Write the contrapositive of “If you are a brunette, then you have brown hair.” If you do not have brown hair, then you are not a brunette. To write a Contrapositive Skill Develop

Think…..Ink…..Share

Survey Says…..

If- Then If an animal is a chimpanzee, then it loves bananas Converse If an animal loves bananas then it is a chimpanzee. Inverse If an animal is not a chimpanzee, then it does not love bananas Contrapositive If an animal does not love bananas then it is not a chimpanzee.

If points are collinear, then they lie on the same line. If points lie on the same line, then they are collinear If points do not lie on the same line, then they not collinear. If- Then Converse Inverse Contrapositive If points are not collinear, then they do not lie on the same line. Complete the Following--CFU

Write the converse of the following statements. State whether the converse is TRUE or FALSE. If FALSE, give a counterexample: “If you are at least 16 years old, then you can get a driver’s license.” If _______________________, then _______________________. you can get a driver’s license you are at least 16 years old “If today is Saturday, then there is no school. If _______________, then ______________. there is no school today is Saturday TRUE! FALSE! We don’t have school on New Years day which may fall on a Monday.

2.The lawn is mowed and the $10 is not paid. The promise is not kept so the conditional is false. 4.The lawn is not mowed and the $10 is not paid. The promise is not broken since the lawn was not mowed, so the conditional is still true. 3.The lawn is not mowed and the $10 is paid. The promise is kept, so the conditional is true. 1.The lawn is mowed and the $10 is paid. The promise is kept so the conditional is true. A conditional statement uses the words if…then. It is like making a promise. In logic, if the “promise” is broken, and not kept, the conditional is said to be false. Otherwise, it is true. Consider the statement: “If you mow my lawn, then I will pay you $10.” (p  q) There are four situations possible. The Conditional pq p  q TTT TFF FTT FFT Read “If p then q”

right

true right perpendicular linear pair adjacent false

How will we use these definitions?

Performance Task

What was the Objective? Students will analyze statements, write definitions as conditional statements and verify validity. Why? So you can verify statements, as seen in Ex 2. Mastery is 80% or better on 5-min checks and indy work.

Homework Students will write and test validity of conditional statements and their converses. Pages #2-28 Even