2-6 Algebraic Proof

Report
2-6 Algebraic Proof
Ms. Andrejko
Real World
 Mythbusters
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
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
Examples – Find property
 State the property that justifies each statement:
1.
If 80 = m∠A, then m∠A = 80.
Reflexive Property of Equality
2.
If RS = TU and TU = YP, then RS = YP
Transitive Property of Equality
Practice – Find property
 State the property that justifies each statement:
1.
If 7x = 28, then x = 4.
Division Property of Equality
2.
If VR + TY = EN + TY, then VR = EN.
Subtraction Property of Equality
3.
If m∠1 = 30 and m∠1 = m∠2, then m∠2 = 30.
Transitive Property of Equality
Example – Fill in proof
Given
Subtraction Prop.
6x -5 = 1
6x -5 +5 = 1 +5
Substitution Prop.
Division Prop.
X=1
Substitution Prop.
Practice – Fill in the Proof
Given: DF ≅ EG
Prove: x=10
STATEMENTS
REASONS
a. DF ≅ EG
a. Given
b. DF = EG
c. 11 = 2x-9
b. Definition of
Congruence
c. Substitution Prop.
d. 11+9 = 2x-9+9
d. Addition prop.
e. 20 = 2x
f. (20/2) = (2x/2)
g. 10 = x
Substitution Prop.
f. Division Prop.
Substitution Prop.
Practice – Fill in proof
Given: 8  3 x  32
4
Prove: x = - 40
Proof:
STATEMENTS

a.
8  3x
b.
a. Given
 32
4
If 
1
REASONS
n  12
b. Multiplication Prop.
3

c.
8-3x = 128
c.
Substitution Prop.
d. 8-3x-8 = 128-8
d. Subtraction property
e. -3x = 120
e. Substitution Prop.
f. X = - 40
f. Division Prop.

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