1. Deductive Reasoning “Indubitably.” “The proof is in the pudding.”
Le pompt de pompt le solve de crime!"
Deductive Reasoning
Je solve le crime. Pompt de pompt pompt."

2. Proving Theorems Written form Simplistic form
The Midpoint Theorem
If m is the midpoint of , then
Written form A M B
Simplistic form
Hypothesis
Given:
Conclusion
Prove:

3. Proving Theorems Given: Prove: Statements Reasons The Midpoint TheoremB
Def of mp
Def of mp
Statements
Reasons
Given
AM = MB
Definition of midpoint
AM + MB = AB
Segment Addition Post.
AM + AM = AB
Substitution
2 AM = AB
Combine like terms
__ __
Mental step
Division Prop. of Equality

4. Please be patient!!! Let’s begin.
As you continue to learn to prove theorems, it is important to get accustomed to the various forms of stating a theorems.
You need to get accustomed to using the hypothesis and the conclusion.
This will take time. You will be given enough time.
You are learning a new way of thinking. Understanding the importance of this type of thinking will take even more time.
Please be patient!!! Let’s begin.

5. These proofs are using deductive reasoning.
Deductive reasoning is a linking of
cause and effect statements to reach a conclusion.
It is like a chain that starts and moves to other the end.
Beginning
Hypothesis
Given
End
Conclusion
To Prove

6. It is also like a row of dominos.
Like dominos which have two blocks on each tile, each step of the proof also has two parts – statements and reasons.
Statements without reasons are
not valid or substantiated.
Each line of the proof must contain a statement supported by a reason or justification.
When this happens, the hypothesis logical forces you to accept the conclusion just like a row of dominos being toppled.

7. How are we going to learn how to do proofs?
1] Examine the structure of completed proofs.
2] Fill in the reasons for steps of partially completed proofs.
3] Fill in proofs that have blanks on either the statement or the reason side.
4] Do our own proofs with simple geometry and simple algebra.

8. How many proofs will we do?
This is a slow very process.
However, it is relatively painless. It leads to success and understanding.
How many proofs will we do?
How many swings at a baseball before you are a good hitter?

9. Substitution Prop. Of Equality
Given:
Prove: ? ?
Label diagram to help visualize.
Statements Reasons
Given
Angle Add. Postulate
Angle Add. Postulate
Substitution Prop. Of Equality
Reflexive Prop. Of Equality
Subtr. Prop. Of Equality

10. ? ? g Given: Prove: g g g Given Given Addition Prop. Of Equality
Label diagram to help visualize.
Statements Reasons
Given
Given
Addition Prop. Of Equality
Angle Add. Postulate
Angle Add. Postulate
Substitution Prop. Of Equality

11. W L g K ? WK = RN LK = RU g g ? WL = UN R U N g Given Given: Prove:
Label diagram to help visualize.
Statements Reasons
WK = RN
Given WK
____ = WL + LK
Segment Add. Postulate RN
Segment Add. Postulate
____ = RU + UN
Substitution Prop. Of Equality
WL + LK = RU + UN
Given
LK = RU
Subtr. Prop. Of Equality
WL = UN

12. W L g K ?
Notice that the given doesn’t have to come first. You can put it in when it is needed. g g ? R U N g
Statements Reasons
Given
WK = RN WK
____ = WL + LK
Segment Add. Postulate RN
Segment Add. Postulate
____ = RU + UN
Substitution Prop. Of Equality
WL + LK = RU + UN
Given
LK = RU
Subtr. Prop. Of Equality
WL = UN

13. Let’s try an alternate approach to the same problem.

14. W L g K ? WK = RN LK = RU g g ? WL = UN R U N g Given: Prove: Given
Label diagram to help visualize.
Statements Reasons
Given
WK = RN
LK = RU
Given WK
____ = WL + LK
Segment Add. Postulate RN
____ = RU + UN
Segment Add. Postulate
WL + LK = RU + UN
Substitution Prop. Of Equality
Subtr. Prop. Of Equality
WL = UN

15. Did you notice that it was not as easy to follow?
It is not wrong. But understanding is more difficult. In geometry there are often many correct approaches to the same problem.
If you find it easier to put the given down first. Do it. Eventually, you will learn easier ways to do your proofs.
It is not uncommon to be able to complete
only 50% of yourproofs

16. It is not uncommon to be able to complete only 50% of your homework
It is not uncommon to be able to complete only 50% of your homework. This is the nature of geometry in the beginning. Do not feel bad.
Many students experience frustration in the beginning. Persevere and the frustration will disappear.

17. C’est fini.
Good day and good luck.