1. Chapter 2 Review
Geometric Reasoning

2. 2.1 Inductive Reasoning Vocabulary: Tasks:
Inductive Reasoning → reasoning based on patterns
Conjecture → statement you believe to be true
Counterexample → example that shows a conjecture is false.
Tasks:
Use patterns to find the next term in a pattern.
Given information, write a conjecture.
Provide counterexamples to false statements.

3. 2.2 Conditional Statements
Vocabulary:
Conditional Statements : if-then statements (p →q)
Hypothesis: “If” part of conditional statement (p)
Conclusion: “Then” part of conditional statement (q)
Converse: q → p
Inverse : ~p → ~q
Contrapositive : ~q → ~p
Tasks:
Write conditional statements
Identify the hypothesis and conclusion
Write and/or identify the inverse, converse or contrapositive. Determine if they are true or false. If false provide a counterexample.

4. 2.3 Deductive Reasoning Vocabulary: Tasks
Deductive reasoning: reasoning based on facts.
Tasks
Verify correct use of/use Law of Detachment
If there is precipitation and the temperature is below 32F, then it will snow. It is snowing.
CONJECTURE: There is precipitation and the temperature is below 32F.
Why is this invalid? What would a valid use of detachment say?
Law of Syllogism
If an animal is a duck, then it has webbed feet. If an animal has webbed feet, then it can swim. A Mallard is a duck. Write an appropriate conclusion.

5. 2.5 Algebraic Proofs
Algebraic Properties (p. 11)

6. 2.6/7: Geometric Proofs Given: Prove: is a right angle. Statements1  2 B A C 3
Given:
is a right angle.
Prove:
are complementary.
Statements
Reasons
is a right angle.
1. Given 2.
2. Definition of right angle 3. 4. 5.
5. Definition of congruent angles 6. 7.
7. Definition of complementary
mBAC = 90
Angle Addition Postulate
Substitution Prop.
m  m
Substitution Prop.
   are comp.

7. Given: m  mR    Prove: 2  31 Q P N M O R • 3 4
Given: m  mR
  
Prove: 2  3
Statements
Reasons 1.
Given
2. m = m 2.
3. m+ m = mMOP
m3+ m4 = mROP 3.
4. m+ m =90
m3+ m4 =90 4. 5.
5. Transitive Property
6. m+ m = m3+ m1 6. 7.
7. Subt. Prop. =
8. 2  3 8.
m  mR
  
Def. of 
 add. Post.
Substitution Prop.
m1 + m2  m3 + m4
Substitution Prop.
m2  m3
Def. of 

8. Prove:  is supplementary to 1 4 3 k 2
Given:   
Prove:  is supplementary to 
Statements
Reasons
1.    1.
2. m = m 2.
3.   are supplementary
3 4 are supplementary 3.
4. m+ m =180
m3+ m4 =180 4.
5. m+ m = m3+ m4 5.
6. m+ m = m3+ m1 6.
7. m = m3 7.
8. m+ m3 =180 8.
9.  is supplementary to  9.
Given
Def. of 
Linear Pair Theorem
Def. of supplementary
Transitive Property (substitution prop)
Substitution Property
Subtraction Prop. Of =
Substitution Property
Def. of supplementary