1. Algebra
3.4 Algebra Properties

2. Geometry 2.4 Reasoning with Algebra Properties
Goals
Use properties from algebra.
Use properties to justify statements.
March 27, 2017
Geometry 2.4 Reasoning with Algebra Properties

3. Geometry 2.4 Reasoning with Algebra Properties
Don’t copy all of this down
You have had most before. Copy the ones that are new to you
You need to have them all memorized.
This as well as all presentations are available on-line.
March 27, 2017
Geometry 2.4 Reasoning with Algebra Properties

4. Geometry 2.4 Reasoning with Algebra Properties
Addition Property
Addition Property
If a = b, then a + c = b + c.
Example
x – 12 = 15
x – =
x = 27
March 27, 2017
Geometry 2.4 Reasoning with Algebra Properties

5. Geometry 2.4 Reasoning with Algebra Properties
Subtraction Property
Subtraction Property If a = b, then a – c = b – c
Example
x + 30 = 45
x + 30 – 30 = 45 – 30
x = 15
March 27, 2017
Geometry 2.4 Reasoning with Algebra Properties

6. Multiplication Property
If a = b, then ac = bc
Example
March 27, 2017
Geometry 2.4 Reasoning with Algebra Properties

7. Geometry 2.4 Reasoning with Algebra Properties
Division Property
Division Property
Example
March 27, 2017
Geometry 2.4 Reasoning with Algebra Properties

8. Geometry 2.4 Reasoning with Algebra Properties
Other Properties
Reflexive Property For any number a, a = a.
Symmetric Property If a = b, then b = a.
Transitive Property If a = b and b = c, then a = c
Substitution Property If a = b and a = c, then b = c
Distributive Property a(b + c) = ab + ac
March 27, 2017
Geometry 2.4 Reasoning with Algebra Properties

9. Geometry 2.4 Reasoning with Algebra Properties
Identify the Property
If 43 = x, then x = 43.
Property?
Symmetric
March 27, 2017
Geometry 2.4 Reasoning with Algebra Properties

10. Geometry 2.4 Reasoning with Algebra Properties
Identify the Property
If 3x = 12, then 12x = 48
Property?
Multiplication
March 27, 2017
Geometry 2.4 Reasoning with Algebra Properties

11. Geometry 2.4 Reasoning with Algebra Properties
Identify the Property
If x = y, and y = 10, then x = 10
Property?
Transitive
March 27, 2017
Geometry 2.4 Reasoning with Algebra Properties

12. Geometry 2.4 Reasoning with Algebra Properties
Identify the Property
If x = 12, then x + 2 = 14
Property?
Addition
March 27, 2017
Geometry 2.4 Reasoning with Algebra Properties

13. Geometry 2.4 Reasoning with Algebra Properties
Using a Property
Addition Property:
If n = 14, then n + 2 = _________ 16
March 27, 2017
Geometry 2.4 Reasoning with Algebra Properties

14. Geometry 2.4 Reasoning with Algebra Properties
Using a Property
Symmetric:
If AB = CD, then CD = ________ AB
March 27, 2017
Geometry 2.4 Reasoning with Algebra Properties

15. Geometry 2.4 Reasoning with Algebra Properties
Using a Property
Transitive:
If mA = mB, and mB = mC,
then mA = _________.
mC
March 27, 2017
Geometry 2.4 Reasoning with Algebra Properties

16. Geometry 2.4 Reasoning with Algebra Properties
Justification
One of the main reasons to study Algebra is to learn how to prove things. The whole business of math is proving things.
To prove things in math you must be able to justify everything with legitimate reasons.
Our reasons include: postulates, definitions and algebra properties.
March 27, 2017
Geometry 2.4 Reasoning with Algebra Properties

17. Geometry 2.4 Reasoning with Algebra Properties
Example
Solve 3x + 12 = 8x – 18 and write a reason for each step.
3x + 12 = 8x – 18
Given
3x – 8x + 12 – 12 = 8x – 8x – 18 – 12
Subtraction Property
–5x = –30
Simplify (combine like terms)
–5x/(–5) = –30/(–5)
Division Property
x = 6
Simplify
March 27, 2017
Geometry 2.4 Reasoning with Algebra Properties

18. Another Example (w/o intermediate steps)
Solve x+2(x – 3) = 5x + 2
x + 2(x – 3) = 5x + 2
Given
x + 2x – 6 = 5x + 2
Distributive Prop.
3x – 6 = 5x + 2
Simplify
3x = 5x + 8
Addition Prop.
–2x = 8
Subtraction Prop.
x = – 4
Division Prop.
March 27, 2017
Geometry 2.4 Reasoning with Algebra Properties

19. Geometry 2.4 Reasoning with Algebra Properties
Before we do a proof…
Given
Any algebra proof must begin with information that we know is true. This will be given to us as a place to start, so it is called the “given”. There can be one or more givens in a problem.
March 27, 2017
Geometry 2.4 Reasoning with Algebra Properties

20. Geometry 2.4 Reasoning with Algebra Properties
This is “Proof”.
If you feel uncomfortable and confused, that’s normal. Everyone is confused with proof at first.
There is only one way to learn proof: PRACTICE.
You have to know the properties, postulates and definitions.
You must diligently practice by doing the homework every night – NO EXCUSES.
You learn by making mistakes. Everyone does.
March 27, 2017
Geometry 2.4 Reasoning with Algebra Properties

21. Geometry 2.4 Reasoning with Algebra Properties
Proof is essential.
Proof is a mandatory part of higher math. If you plan on going to college and/or taking more advanced math you must prove things. Algebra is the place to learn to do this.
We will do proofs until the end of the year. Don’t fight it, they are not going to go away.
March 27, 2017
Geometry 2.4 Reasoning with Algebra Properties