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

2. 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.

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

4. 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

5. 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 .

6. 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!

7. 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:

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

9. 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

10. 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.

11. 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.

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

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

14. “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?

15. “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?

16. “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?

17. 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)

18. 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)