Equality Example

Transitive Property of Equality Variation 1

Divide Both Sides

Multiply Substitute Two Terms

Multiply Substitute Two Terms 2

Zero Plus a

Transitive Property of Equality Variation 2

Multiplicative Property of Equality Variation 2

Transitive Property of Equality Variation 3

Division is Commutative

Associative Property

Multiplicative Property of Equality Variation 1

Simplify

Transitive

Distributive Property 2

Commutative Property Variation 1

Substitution 2

Substitution 6

Distributive Property 3

Associative Property of Multiplication 2

Transitive Property Application 2

Substitution 10

Substitution 12

Divide Simplify 2

Simplify 2

Simplify 3

Transitive 2

Subtract Same Sides

Divide Both

Divide Substitute 2

Divide Substitute 4

Slope 1

Subtract Zero Example

Subtraction Example

Subtract to Zero

Example 2

Subtract Associative

Subtract 1

Divide Zero 2

Midsegment Triangle

Proof: Substitution 12

Let's prove the following theorem:

if the following are true:

a = b ⋅ c
c = d

then a = b ⋅ d

Proof:

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Given

1	a = b ⋅ c
2	c = d

Proof Table

#	Claim	Reason
1	b ⋅ c = b ⋅ d	if c = d, then b ⋅ c = b ⋅ d (Multiplicative Property of Equality Variation 1)
2	a = b ⋅ d	if a = b ⋅ c and b ⋅ c = b ⋅ d, then a = b ⋅ d (Transitive Property of Equality)

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