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

 1.

State the property that justifies each statement: 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

 1.

State the property that justifies each statement: 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

6x -5 = 1 6x -5 +5 = 1 +5 X=1 Given Subtraction Prop.

Substitution Prop.

Division Prop.

Substitution Prop.

Practice – Fill in the Proof Given: DF ≅ Prove: x=10 EG

STATEMENTS a. DF

≅

EG

b.

DF = EG c. 11 = 2x-9

d.

11+9 = 2x-9+9

e. 20 = 2x f.

(20/2) = (2x/2)

g.

10 = x REASONS

a.

Given

b. Definition of Congruence

c.

Substitution Prop.

d. Addition prop.

Substitution Prop.

f. Division Prop.

Substitution Prop.

Practice – Fill in proof

Given: 8  4 3

x

 Prove: x = - 40 32  Proof:

STATEMENTS

 a. 8  3

x

4  32 b.

If

 1 3

n

 12 c. 8-3x = 128 a. Given

REASONS

b.

Multiplication Prop.

c.

Substitution Prop.

d.

8-3x-8 = 128-8

d. Subtraction property e. -3x = 120 f. X = - 40 e.

Substitution Prop.

f.

Division Prop.