Lesson 2-1 Conditional Statements

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Lesson 2-1

Conditional

Statements

This is a quiz!!! There should be NO talking

Lesson 2-1 Conditional Statements

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- 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.

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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……

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Lesson 2-1 Conditional Statements

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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 conclusion is the part of an if-then statement that follows “then” (when written in if-then form.)

The hypothesis is the given information, or the condition.

The conclusion is the result of the given information.

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Conditional statements can be written in “if-then” form to emphasize which part is the hypothesis and which is the conclusion.

Writing Conditional Statements

Hint: Turn the subject into the hypothesis.

Example 1: Vertical angles are congruent. can be written as...

If two angles are vertical, then they are congruent.Conditional Statement:

Example 2: Seals swim. can be written as...Conditional Statement: If an animal is a seal, then it swims.

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

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Lesson 2-1 Conditional Statements

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Symbolic Logic

Symbols for Hypothesis and Conclusion:

Hypothesis is represented by “p”.

Conclusion is represented by “q”.

if p, then q or

p implies qContinued…..

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Symbolic Logic - continued

if p, then q

or p implies q

is used to representp q

Example: p: a number is prime q: a number has exactly two divisors

If a number is prime, then it has exactly two divisors.pq:

Continued…..

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Converse

Converse: Switch the hypothesis and conclusion (q p)

pq If two angles are vertical, then they are congruent.

qp If two angles are congruent, then they are vertical.

Continued…..

Name the converse, and then determine if the converse is true or false

1) If you are a quaterback, then you play football.

2) If an angle measures 100 degress, then it is obtuse.

3) If an angle is acute, then it measures greater than 0, but less than 90 degrees.

Lesson 2-1 Conditional Statements

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Lesson 2-1 Conditional Statements

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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.

If you live in Alabama, then you live in Mobile.Statement:

Counterexample: You live in Alabama, BUT you live in Trussville.

Is there a counterexample?

Therefore () the statement is false.

Yes !!!

Determine if the conditional is true or false. If it is false, find a counter example.

1) If a polygon has eight sides, then it is an octagon.

2) If you live in a country that borders the United States, then you live in Canada.

3) If you play a sport with a ball and a bat then you play baseball.

4) If an angle measures 80, then it is acute.

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Lesson 2-1 Conditional Statements

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If …Then vs. Implies

Two angles are vertical implies they are congruent.

Another way of writing an if-then statement is using the word implies.

If two angles are vertical, then they are congruent.

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.

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Lesson 2-1 Conditional Statements

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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?

Each conditional statement below is true. Write its converse. If the converse is also true, combine the statements as a biconditional.

1) If two segments have the same length, then they are congruent.

2) If x=12, then 2x – 5 = 19.

3) If a number is divisible by 20, then it is even.

4) If a ray is an angle bisector, then it divides an angle into two congruent angles.

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Home Work

Pg 75 # 9-21 (skip #14)

Pg 82 # 1-5

Pg 83 # 20-27

Lesson 2-1 Conditional Statements

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Lesson 2-1 Conditional Statements

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