Section 2-2: Conditional Statements

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Section 2-2: Conditional Statements

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Section 2-2: Conditional Statements Rigor: Identify the hypothesis and conclusion of a conditional statement; state truth values and counterexamples Relevance: Logical reasoning

Making Conjectures Conjecture – a statement you believe to be true based on observed patterns. Make a conjecture about the number of triangles formed in a polygon compared to the number of sides the polygon has.

Explore logic with Venn diagrams Turn to page 57 Explore #1

Vocab: Conditional Statements Conditional statement – an if –then statement Hypothesis – the part p following if. Conclusion – the part q following then. p  q ~P means NOT P

2. If you don’t have music, then life would . Underline the hypothesis and box the conclusion for each bumper sticker 1. If you follow me too closely, then I will flick a booger on your windshield. 2. If you don’t have music, then life would .

Writing a conditional statement Step 1: Identify hypothesis and conclusion Step 2: Write “if…, then…” statement. Don’t forget to use a noun before the pronoun!

Example 1: Step 1: box hypothesis, underline conclusion Step 2: Write “Vertical angles are congruent.” as a conditional statement. Step 1: box hypothesis, underline conclusion Step 2:

Example 2: Write “Dolphins are mammals.” as a conditional statement.

Truth Values Conditional statements can be either TRUE or FALSE. True Statements: Given the hypothesis is true, the conclusion MUST ALWAYS be true False Statements: If you can name even ONE example that satisfies the hypothesis but is different from the conclusion, the whole statement is false

Counter Examples Counter Example – an example that proves a statement is false. Example: If a line goes through the midpoint of a segment, then it must be a perpendicular bisector. False! Counterexample - A line going through the midpoint at a 45o angle would satisfy the hypothesis but would not be perpendicular to the line, so is different from the conclusion.

Example: T or F? Give a counterexample for if statement is F. 1. If a month has 28 days, then it is February. 2. If two angles form a linear pair, then they are supplementary.

Another type of logic statement Converse – “If q, then p” - flip the if and then parts of a conditional statement

Example: Conditional: Converse: Truth values don’t have to be the same for both logic statements!

“If I play on a soccer team, then I’m an athlete.” What is the converse to this conditional? What are the truth values of each?

“If a polygon is a square, then it is a rectangle” What is the converse of the conditional statement? What are the truth values of each?

“If the shape has 3 angles, then it is a triangle.” What is the converse of the conditional statement? What is the truth value of each?

2 – 2 Honors Assignments Primary Assignment: Quizizz Period 1: Submit answers online: join.quizizz.com Codes: Period 1: Period 5: Period 6: Secondary Assignment: Workbook pg 59 #1 – 4, 6 – 10; Pg 60 # 1, 6 (do not do inverses or contrapositives)

2 – 2 Standard Assignments Primary Assignment: Quizizz Submit answers online: join.quizizz.com Codes: Period 2: Period 4: Period 7: Secondary Assignment: Workbook pg 59 #1 – 4, 6 – 10; Pg 60 # 1, 6 (do not do inverses or contrapositives)