1. Chapter 2 Deductive Reasoning

2. Chapter 2 Deductive Reasoning page 32
Essential Question
Can you justify the conclusion of a conditional statement?

3. Lesson 2-1 If-Then Statements (page 33)
Essential Question
Can you justify the conclusion of a conditional statement?

4. If-Then Statement: a statement whose basic form is If p, then q.
Also know as conditional statements or conditionals .
Example: If it is snowing, then it is cold.
Conditional statements are either true or false .

5. HYPOTHESIS (p)
a statement that follows the “ If ” in a “If-then” statement.
If it is snowing, then it is cold.
Example: It is snowing.

6. CONCLUSION (q)
a statement that follows the “ then ” in a “If-then” statement.
If it is snowing, then it is cold.
Example: It is cold.

7. Forms for Conditional Statements:
If it is snowing, then it is cold.
It is snowing implies it is cold.
It is snowing only if it is cold.
It is cold if it is snowing.
Circle one: TRUE or FALSE
If p, then q.
p implies q.
p only if q.
q if p.

8. If, then, implies, and only if are NOT part of the
NOTE:
If, then, implies, and only if
are NOT part of the
hypothesis or the conclusion.

9. Example:
If angle X is acute, then the measure of angle X equals 60 degrees.
∠X is acute implies the m∠ X = 60º .
∠X is acute only if the m∠ X = 60º .
The m∠ X = 60º if ∠X is acute .
Circle one: TRUE or FALSE

10. CONVERSE (of a conditional statement)
is formed by interchanging the hypothesis and the conclusion.
Converses are either true or false .

11. If it is cold , then it is snowing .
Example:
CONDITIONAL …
If it is snowing, then it is cold.
CONVERSE …
If it is cold , then it is snowing .
Circle one: TRUE or FALSE
If p, then q.
If q, then p.

12. Example:
CONDITIONAL …
If angle X is acute, then the measure of angle X equals 60 degrees.
CONVERSE …
If the m∠ X = 60º , then ∠X is acute .
Circle one: TRUE or FALSE
If p, then q.
If q, then p.

13. Please take note …
You can not assume a converse is true just because the original statement is true.

14. NOTE: only one counterexample is needed to prove a statement false!
an example used to prove that an if-then statement is false .
The hypothesis is true and the conclusion is false .
NOTE: only one counterexample is needed to prove a statement false!

15. Example: Two angles are adjacent if they have a common vertex.
CONDITIONAL …
If 2∠’s have a common vertex ,
then they are adj. ∠’s .
TRUE or FALSE
Draw or write a counterexample …

16. Example: Two angles are adjacent if they have a common vertex.
CONVERSE …
If 2∠’s are adj. ∠’s ,
then they have a common vertex.
TRUE or FALSE
NO counterexample is necessary since it is TRUE.

17. BICONDITIONAL
a statement that combines a conditional and its converse with the words “ if and only if ”. (iff)

18. then their measures are equal.
Example:
CONDITIONAL …
If two angles are congruent,
then their measures are equal.
BICONDITIONAL …
Two angles are congruent if and only if their measures are equal.
p ⇒ q
p ⟺ q

19. Can you justify the conclusion of a conditional statement?
Assignment
Written Exercises on page 35
RECOMMENDED: 3, 5, 7, 9. 30, 31
REQUIRED: 12, 15, 16, 18, 21, 24, 27
Can you justify the conclusion of a conditional statement?