1. 2-6 Algebraic Proof
Ms. Andrejko

2. Real World
Mythbusters

3. Vocabulary
Algebraic Proof- uses a group of algebraic steps to solve problems and justify each step.
Two-column proof/formal proof- contains statements and reasons organized into 2 columns

4. Properties (see handout)
Addition property of equality
Subtraction property of equality
Multiplication property of equality
Division property of equality
Reflexive property of equality
Symmetric property of equality
Transitive property of equality
Substitution property of equality
Distributive property

5. Examples – Find property
State the property that justifies each statement:
If 80 = m∠A, then m∠A = 80.
If RS = TU and TU = YP, then RS = YP
Reflexive Property of Equality
Transitive Property of Equality

6. Practice – Find property
State the property that justifies each statement:
If 7x = 28, then x = 4.
If VR + TY = EN + TY, then VR = EN.
If m∠1 = 30 and m∠1 = m∠2, then m∠2 = 30.
Division Property of Equality
Subtraction Property of Equality
Transitive Property of Equality

7. Example – Fill in proof Given Subtraction Prop. 6x -5 = 1
Substitution Prop.
Division Prop.
X=1
Substitution Prop.

8. Practice – Fill in the Proof
STATEMENTS
REASONS
a. DF ≅ EG a. b.
b. Definition of Congruence
c. 11 = 2x-9 c. d.
d. Addition prop.
e. 20 = 2x f.
f. Division Prop. g.
Given
DF = EG
Substitution Prop.
Given: DF ≅ EG
Prove: x=10
11+9 = 2x-9+9
Substitution Prop.
(20/2) = (2x/2)
10 = x
Substitution Prop.

9. Practice – Fill in proof
Given: Prove: x = - 40 Proof:
STATEMENTS
REASONS a.
a. Given b.
c x = 128 c. d.
d. Subtraction property
e. -3x = 120 e.
f. X = - 40 f.
Multiplication Prop.
Substitution Prop.
8-3x-8 = 128-8
Substitution Prop.
Division Prop.