1. What is a Proof? Pg. 19 Types of Proof
3.6
What is a Proof?
Pg. 19
Types of Proof

2. 3.6 – What Is A Proof?
Types of Proof
Whenever you buy a new product that needs to be put together, you are given a set of directions. The directions are written in a specific order that must be followed closely in order to get the desired finished product. Sometimes they clarify their directions by explaining why you are completing each step. This is the same idea we use in geometry in proofs.

3. 3.31 – ORDERING STATEMENTS
When you write a proof, the statements must be in a specific order, building off of each other. You can't just jump to the end without breaking down each part. To illustrate this, with your group explain how to make a peanut butter and jelly sandwich. Work with your team to include all steps to make sure the sandwich will be made correctly.

4. 3.32 – STATEMENTS AND REASONS
When you write a proof in geometry, each statement you make must have a reason to support it. This helps people understand why each statement was listed. This can be done in a flowchart proof or a two-column proof. Examine the two types below. Notice where the statements and reasons are. Also, notice how the statements are in a specific order.

7. 4.3 – REASONS
The reasons for certain statements come from definitions, properties, postulates, and theorems. Below are some commonly used reasons.

8. a + c = b + c a - c = b - c ac = bc a/c = b/c ax + ab Name
Property of Equality
Addition Property
If a = b, then
Subtraction Property
Multiplication Property
Division Property
Distribution Property
If a(x + b), then
a + c = b + c
a - c = b - c
ac = bc
a/c = b/c
ax + ab

9. a = a If a = b, then b = a a = c b can replace a Substitution Property
Reflexive Property
Symmetric Property
Transitive Property
If a = b and b = c, then
b can replace a
a = a
If a = b, then
b = a
a = c

10. 1. Use the property to complete the statement.

11. a. Write the reason for each statement

12. Statement
Reason
If 4(x + 7), then 4x + 28
If 2x + 5 = 9, then 2x = 4
If x – 7 = 2, then x = 9
If 4x = 12, then x = 3
Distributive Prop.
Reflexive Prop.
Subtraction Prop.
Transitive Prop.
Addition Prop.
Symmetric
Division Prop.

13. PROOFS!
All proofs start and end the same. It is very helpful to have a picture to refer to. We are given information and then are told to prove something.

14. Format of Proofs
Given:
Picture
Prove:
Statements Reasons 1. 2. 3. …
What you are given 1. 2. 3. …
Given
To Prove

15. given Addition Prop Division Prop Statements Reasons 1. 8x – 34 = 6
Complete the logical argument by writing a reason for each step.
Statements
Reasons
x – 34 = 6
1. __________________
x = 40
2. __________________
x = 5
3. __________________
given
Addition Prop
Division Prop

16. given Subtraction Prop Addition Prop Division Prop Statements Reasons
Complete the logical argument by writing a reason for each step.
Statements
Reasons
x – 7 = 6x + 7
1. __________________
x – 7 = 7
2. __________________
x = 14
3. __________________
x = -7
4. __________________
given
Subtraction Prop
Addition Prop
Division Prop

17. given Distributive Prop Subtraction Prop Addition Prop
Complete the logical argument by writing a reason for each step.
Statements
Reasons
(x – 3) = 4(x + 2)
1. _______________________
x – 15 = 4x + 8
2. _______________________
x – 15 = 8
3. _______________________
x = 23
4. _______________________
given
Distributive Prop
Subtraction Prop
Addition Prop

18. 4. Solve the equation. Write a reason for each step 4x – 9 = 2x + 11
Statements
Reasons 1.
4x – 9 = 2x + 11 1.
Given 2.
2x – 9 = 11 2.
Subtraction Prop. 3.
2x = 20 3.
Addition Prop. 4.
x = 10 4.
Division Prop.

19. 3.33 Solve the equation for y. Write a reason for each step.
12x – 3y = 30
Statements
Reasons 1.
12x – 3y = 30 1.
Given 2.
–3y = -12x + 30 2.
Subtraction Prop. 3.
y = 4x – 10 3.
Division Prop.

20. C. Given E. Reflexive F. Addition Prop. A. Segment Addition
3.34 – GEOMETRIC PROOF
Complete the proof by writing a reason for each step.
GIVEN: AL = SK
PROVE: AS = LK
C. Given
E. Reflexive
F. Addition Prop.
A. Segment Addition
D. Segment Addition
B. Substitution

22. given
Def. of Midpoint
given
Segment Addition
Substitution
Substitution
Simplify

24. given
Def. Segment Bisector
given
Segment Addition
Substitution
Substitution
Simplify

26. 1. 1. Given 2. 2. 3. 3. given 4. 4. Angle Addition 5. 5. Substitution
Statements
Reasons 1. 1.
Given 2. 2.
Def. of angle bisector 3. 3.
given 4. 4.
Angle Addition 5. 5.
Substitution 6. 6.
Substitution 7. 7.
Simplify