1. 2-4 Deductive Reasoning
8th Grade Geometry

2. Conditional Statement (If-then) - If p, then q (p  q)
Converse – If q, then p (q  p)
Inverse – If not p, then not q (~ p  ~q)
Contrapositive – If not q, then not p (~q  ~ p)
Biconditional Statement (if and only if) – p if and only if q (p  q)

3. Conditional Statement (If-then) –
If p, then q.
Symbols: p  q

4. Inductive Reasoning – reasoning based on patterns
Deductive Reasoning – reasoning based on using given facts.

5. If an “If-Then” statement and its Hypothesis are true,
Law of Detachment:
If an “If-Then” statement and its Hypothesis are true,
then the Conclusion is true.

6. There are clouds in the sky.
Malcolm earns an A.
Angles 3 and 4 are congruent.
d. Given: If two angles are vertical, then they are congruent. Angles 3 and 4 are supplementary.
No conclusion.

7. Law of Syllogism: If pq and qr are both true, then pr is true.
Example: If it is July, then you are on summer vacation. If you are on summer vacation, then you work at an ice-cream shop.
Conclusion: If it is July, then you work at an ice-cream shop.

8. If a number is divisible by 12, then it is divisible by 3.
No Conclusion

9. Ken lives in the United States.