1. Warm Up Write a conclusion to match the hypothesis:
If I ride my bike down that steep hill, then _____________________
If an angle measures exactly 180 degrees, then ________________
Write a hypothesis to match the conclusion:
_______________________________ then I am probably dreaming.
_______________________________ then they are adjacent angles.

2. Conditional Statements
Part 2

3. Review..
Conditional statement – logical statement that has two parts, a hypothesis (p), and a conclusion (q).
Written in “if – then” form, the “if” part contains the hypothesis, and the “then” part contains the conclusion
In words: If p, then q
In math symbols: p q
If Clark is a dog, then he has four legs
hypothesis
conclusion

4. Related Conditionals Negation – the opposite of the original statement
In words: “not p” or “not q”
In math symbols: ~p or ~q
Example: The cat is black. (negation) The cat is NOT black
Example: Chuck Norris is not awesome. (negation) Chuck Norris IS awesome.
Converse – to write the converse of a conditional statement, just switch the hypothesis and conclusion
In words: if q then p
In math symbols: q p
Example: If it is raining, then it is wet. (converse) If it is wet, then it is raining.
Example: If x is even, then x is divisible by 2.(converse) If x is divisible by 2, then x is even.

5. Related Conditionals (cont’d.)
Inverse – to write the inverse of a conditional statement, negate both the hypothesis and conclusion
In words: If not p then not q
In math symbols: ~p ~q
Example: If I break my phone I will get grounded. (inverse) If I do not break my phone, I will not get grounded.
Example: If you play guitar, then you are a musician. (inverse) If you do not play guitar, then you are not a musician.

6. Related Conditionals (cont’d.)
Contrapositive – to write the contrapositive of a conditional statement, first write the converse. Then negate both the hypothesis and conclusion.
In words: If not q then not p
In math symbols: ~q ~p
Example: If the year has 366 days then it is a leap year. (contrapositive) If it is not a leap year, then the year does not have 366 days.
Example: If you throw a bucket of ice water on my head, then I will scream. (contrapositive) If I do not scream, then you will not throw a bucket of ice water on my head.

7. Related Conditionals (cont’d.)
Biconditional statement – when a conditional statement and its converse are both true, you can write them as a single biconditional statement. It uses the phrase “if and only if.” These are often used in geometric definitions.
In words: q if and only if q
In math symbols: p q
Example: If an angle is less than 90 degrees, then it is an acute angle. (biconditional) An angle is less than 90 degrees if and only if it is an acute angle.
Example: If two lines intersect to form a right angle, then they are perpendicular lines. (biconditional) Two lines intersect to form a right angle if and only if they are perpendicular lines.