Conditional Statements Lesson 2-1 Conditional Statements Lesson 2-1 Conditional Statements

This is a quiz!!! There should be NO talking Take out a small sheet of paper (it can be torn out) put your name on it. Then identify the hypothesis and the conclusion of the statement below. Statement: If you cheat on this quiz, then you will get a zero. Lesson 2-1 Conditional Statements

Conditional Statements (or simply Conditionals) Definition: A conditional statement is a statement that can be written in if-then form. “If _____________, then ______________.” Example: If your feet smell and your nose runs, then you're built upside down. Continued…… http://www.clevelandnasalsinus.com/Sinus-nasal-disorders-cleveland-nasal-sinus-sleep-ear-nose-throat-ohio.html http://joshhollidayshow.com/?p=647

Conditional Statement - continued Conditional Statements have two parts: The hypothesis is the part of a conditional statement that follows “if” (when written in if-then form.) The hypothesis is the given information, or the condition. The conclusion is the part of an if-then statement that follows “then” (when written in if-then form.) The conclusion is the result of the given information. Lesson 2-1 Conditional Statements

Lesson 2-1 Conditional Statements Writing Conditional Statements Conditional statements can be written in “if-then” form to emphasize which part is the hypothesis and which is the conclusion. Hint: Turn the subject into the hypothesis. Example 1: Vertical angles are congruent. can be written as... Conditional Statement: If two angles are vertical, then they are congruent. Example 2: Seals swim. can be written as... Conditional Statement: If an animal is a seal, then it swims. Lesson 2-1 Conditional Statements

Lesson 2-1 Conditional Statements Examples If the defense doesn’t wake up and learn how to tackle, then Auburn will lose.  If x – 8 = 14, then x = 22. If B is between A and C, then AB + BC = AC Can you think of one? Lesson 2-1 Conditional Statements

Lesson 2-1 Conditional Statements Symbolic Logic Symbols for Hypothesis and Conclusion: Hypothesis is represented by “p”. Conclusion is represented by “q”. if p, then q or p implies q Continued….. Lesson 2-1 Conditional Statements

Symbolic Logic - continued if p, then q or p implies q p  q is used to represent Example: p: a number is prime q: a number has exactly two divisors pq: If a number is prime, then it has exactly two divisors. Continued….. Lesson 2-1 Conditional Statements

Lesson 2-1 Conditional Statements Converse Converse: Switch the hypothesis and conclusion (q  p) pq If two angles are vertical, then they are congruent. qp If two angles are congruent, then they are vertical. Continued….. Lesson 2-1 Conditional Statements

Name the converse, and then determine if the converse is true or false If you are a quaterback, then you play football. If an angle measures 100 degress, then it is obtuse. If an angle is acute, then it measures greater than 0, but less than 90 degrees. Lesson 2-1 Conditional Statements

Conditional Statements can be true or false: A conditional statement is false only when the hypothesis is true, but the conclusion is false. A counterexample is an example used to show that a statement is not always true and therefore false. Statement: If you live in Alabama, then you live in Mobile. Yes !!! Is there a counterexample? Counterexample: You live in Alabama, BUT you live in Trussville. Therefore () the statement is false. Lesson 2-1 Conditional Statements

Lesson 2-1 Conditional Statements Determine if the conditional is true or false. If it is false, find a counter example. If a polygon has eight sides, then it is an octagon. If you live in a country that borders the United States, then you live in Canada. If you play a sport with a ball and a bat then you play baseball. If an angle measures 80, then it is acute. Lesson 2-1 Conditional Statements

Two angles are vertical implies they are congruent. If …Then vs. Implies Another way of writing an if-then statement is using the word implies. If two angles are vertical, then they are congruent. Two angles are vertical implies they are congruent. Lesson 2-1 Conditional Statements

Other ways to write If-Then Statements If-then statements may be written in different ways. These are included on the board or in your book on page 34. Lesson 2-1 Conditional Statements

Lesson 2-1 Conditional Statements Biconditional When a conditional statement and its converse are both true, the two statements may be combined. Use the phrase if and only if (sometimes abbreviated: iff) Statement: If an angle is right then it has a measure of 90. Converse: If an angle measures 90, then it is a right angle. Biconditional: An angle is right if and only if it measures 90. Can you think of an example? Lesson 2-1 Conditional Statements

Lesson 2-1 Conditional Statements Each conditional statement below is true. Write its converse. If the converse is also true, combine the statements as a biconditional. If two segments have the same length, then they are congruent. If x=12, then 2x – 5 = 19. If a number is divisible by 20, then it is even. If a ray is an angle bisector, then it divides an angle into two congruent angles. Lesson 2-1 Conditional Statements

Lesson 2-1 Conditional Statements Home Work Pg 75 # 9-21 (skip #14) Pg 82 # 1-5 Pg 83 # 20-27 Lesson 2-1 Conditional Statements

Lesson 2-1 Conditional Statements