algebraic proof addition:if a = b, then a + c = b + c. subtraction:if a = b, then a - c = b - c....

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Algebraic Proof Addition:If a = b, then a + c = b + c. Subtraction:If a = b, then a - c = b - c. Multiplication: If a = b, then ca = cb. Division: If a = b, and c ≠ 0, then a c = b c

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Page 1: Algebraic Proof Addition:If a = b, then a + c = b + c. Subtraction:If a = b, then a - c = b - c. Multiplication: If a = b, then ca = cb. Division: If a

Algebraic Proof

Addition:If a = b, then a + c = b + c.

Subtraction:If a = b, then a - c = b - c.

Multiplication: If a = b, then ca = cb.

Division: If a = b, and c ≠ 0, then a c = b c

Page 2: Algebraic Proof Addition:If a = b, then a + c = b + c. Subtraction:If a = b, then a - c = b - c. Multiplication: If a = b, then ca = cb. Division: If a

Algebraic Proof

Substitution: If a + b = c and b = d, then a + d = c.

Reflexive: a = a.

Symmetric: If a = b, then b = a.

Transitive: If a = b and b = c, then a = c.

Distributive: a(b + c) = ab + ac.

Page 3: Algebraic Proof Addition:If a = b, then a + c = b + c. Subtraction:If a = b, then a - c = b - c. Multiplication: If a = b, then ca = cb. Division: If a

Algebraic Proof

Deductive Argument – A proof formed by a group of algebraic steps used to solve problems.

• Since geometry also uses variables, numbers, and operations, many of the properties of equality used in algebra are also true in geometry. (Examples: segment measures, angle measures)

Page 4: Algebraic Proof Addition:If a = b, then a + c = b + c. Subtraction:If a = b, then a - c = b - c. Multiplication: If a = b, then ca = cb. Division: If a

Algebraic Proof

Two-column proof (formal proof) – A form of deductive argument with statements and reasons organized in two-columns.

• Each step that advances the argument is called a statement.

• Each property, definition, rule, etc used to justify the statements are called reasons.

Page 5: Algebraic Proof Addition:If a = b, then a + c = b + c. Subtraction:If a = b, then a - c = b - c. Multiplication: If a = b, then ca = cb. Division: If a

Original equation

Algebraic Steps Properties

Distributive Property

Substitution Property

Subtraction Property

Solve

Page 6: Algebraic Proof Addition:If a = b, then a + c = b + c. Subtraction:If a = b, then a - c = b - c. Multiplication: If a = b, then ca = cb. Division: If a

Substitution Property

Division Property

Substitution Property

Answer:

Page 7: Algebraic Proof Addition:If a = b, then a + c = b + c. Subtraction:If a = b, then a - c = b - c. Multiplication: If a = b, then ca = cb. Division: If a

Write a two-column proof for the following.

a.

Page 8: Algebraic Proof Addition:If a = b, then a + c = b + c. Subtraction:If a = b, then a - c = b - c. Multiplication: If a = b, then ca = cb. Division: If a

1. Given

2. Multiplication Property

3. Substitution4. Subtraction Property

5. Substitution

6. Division Property

7. Substitution

Proof:Statements Reasons

1.

2.

3. 4.

5.

6.

7.

Page 9: Algebraic Proof Addition:If a = b, then a + c = b + c. Subtraction:If a = b, then a - c = b - c. Multiplication: If a = b, then ca = cb. Division: If a

If and then which of the following is a valid conclusion?

I.

II.

III.

MULTIPLE- CHOICE TEST ITEM

A I only B I and II C I and III D II and III Answer: C

Page 10: Algebraic Proof Addition:If a = b, then a + c = b + c. Subtraction:If a = b, then a - c = b - c. Multiplication: If a = b, then ca = cb. Division: If a

DRIVING A stop sign as shown below is a regular octagon. If the measure of angle A is 135 and angle A is congruent to angle G, prove that the measure of angle G is 135.

Page 11: Algebraic Proof Addition:If a = b, then a + c = b + c. Subtraction:If a = b, then a - c = b - c. Multiplication: If a = b, then ca = cb. Division: If a

Proof:

Statements Reasons

1. Given

2. Given

3. Definition of congruent angles

4. Transitive Property

1.

2.

3.

4.

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