Chapter 2 Section 6

Algebraic proof

22

Properties of Equality

Addition Property If a = b, then a + c = b + c

Subtraction Property If a = b, then a – c = b – c

Multiplication Property If a = b, then a * c = b * c

Division Property If a = b and c ≠ 0, then a/c = b/c

Reflexive Property 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 b can replace a in any expression

Distributive Property a(b + c) = ab + ac

3

Solve and Write a Justification for Each Step3

6x + 2(x - 1) = 30

6x + 2x - 2 = 30

8x - 2 = 30

8x = 32

8x = 32

8 8

x = 4

Solve 6x + 2(x - 1) = 30 and write a justification for each step:

Given or original equationDistributive Property

Combine Like TermsAddition property

Division property of =

Simplify

This leads to “Proof Writing”

How to Set Up a 2-column Proof

Given:

Prove:

Statement Reason

Diagram

Write a geometric proof

Give a reason for each step

Multiplication

Distributive

Addition

Write a 2-column proof

Distributive

Subtraction

Division

Properties of Congruence Reflexive Property

AB ≅ AB

∠ A ≅ ∠ A

Symmetric Property

If AB ≅ CD, then CD ≅ AB

If ∠ A ≅ ∠ B, then ∠ B ≅ ∠ A

Transitive Property

If AB ≅ CD and CD ≅ EF, then AB ≅ EF

If ∠ A ≅ ∠ B and ∠ B ≅ ∠ C,then ∠ A ≅ ∠ C

Using Properties of Equality and Congruence

State the property that justifies each statement 1.Reflexive

2.Division3.Multiplication

4.subtraction

5.Substitution6.Addition

7.Transitive

1.

2.

3.

4.

5.

6.

7.

Write a 2-column proof

If DF EG, then x = 10 ≅

D E

GF

112x - 9 Statements Reasons

1. DF = EG2. 11 = 2x - 93. 20 = 2x4. 10 = x

1. Given2. Substitution3. Addition4. Division

Write a 2 –column proof

If <Y <Z, then x = 100≅

y

X +10

Z

2x- 90

Statements Reasons

1. <Y = <Z2. x + 10 = 2x - 903. 10 = x - 904. 100 = x

1. Given2. Substitution3. Subtraction4. Addition

Have a great day!