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```2.5 – Reasoning Using Properties of Algebra
Name
Property of Equality
If a = b, then a + c = b + c
Subtraction Property
If a = b, then a – c = b – c
Multiplication
Property
Division Property
If a = b, then ac = bc
Reflexive Property
For any real #, 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, then a/c = b/c
If a = b, then b can be substituted in for a
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.
Format of Proofs
Given:
Prove:
Picture
Statements
Reasons
1. What you are given 1. Given
2.
2.
3.
3.
… To Prove
…
Use the property to complete the statement.
TU + 20
If RS = TU, then RS + 20 = ______________.
3.Multiplication Property of Equality:
If m1 = m2, then 3m1 = ____________.
3m2
4.Substitution Property of Equality:
= 100
If a = 20, then 5a = 5(20)
__________.
5.Reflexive Property of Equality:
x
If x is a real number, then x = _____.
6.Symmetric Property of Equality:
If AB = CD, then CD = __________.
AB
7.Transitive Property of Equality:
If mE = mF and mF = mG, then
________________.
mE = mG
Complete the logical argument by writing a reason for each step.
Statements
1.
8x – 34 = 6
Reasons
1.
given
__________________
2.
8x = 40
2.
__________________
3.
x=5
3.
Division Prop
__________________
Complete the logical argument by writing a reason for each step.
Statements
Reasons
1.
4x – 7 = 6x + 7
1.
given
__________________
2.
-2x – 7 = 7
2.
__________________
Subtraction Prop
3.
-2x = 14
3.
__________________
4.
x = -7
4.
Division Prop
__________________
Complete the logical argument by writing a reason for each step.
Statements
Reasons
1.
5(x – 3) = 4(x + 2)
1.
given
___________________
2.
5x – 15 = 4x + 8
2.
Distributive Prop
__________________
3.
4.
x – 15 = 8
x = 23
3. ___________________
Subtraction Prop
4.
___________________
9. Solve the equation. Write a reason for each step
4x – 7 = 6x + 7
Statements
Reasons
1. 4x – 7 = 6x + 7
1.
Given
– 7 = 2x + 7
2.
Subtraction Prop.
2.
3.
– 14 = 2x
3.
Subtraction Prop.
4.
–7 = x
4.
Division Prop.
10. 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.
Complete the proof by writing a reason for each step.
GIVEN: AL = SK
PROVE: AS = LK
Statements
Reasons
1.
AL = SK
1.
given
___________________
2.
LS = LS
2.
Reflexive Prop
___________________
3. AL + LS = SK + LS
3.
__________________
4.
AL + LS = AS
4. Segment
__________________
5.
SK + LS = LK
5. Segment
___________________
6.
AS = LK
6.
Substitution Prop
___________________
Steps for Proofs: