Properties of Equality
Number Sets
Segments
Real number properties
All about proofs
100

This property states that if a is a real number, then a = a.

What is the reflexive property of equality?

100

This number set:

{1,2,3,...}

What is the set of natural numbers? (N)

100

Given segment A-B-C, AB + BC = AC.

What is the definition of between?

100

This property states that for real numbers a and b,

a + b = b + a

What is the commutative property of addition?

100
A sequence of statements paired with reasons explaining why those statements are true.

What is a two-column proof?

200

This property is illustrated by the following statement

If 10 = x, then x = 10.

What is the symmetric property of equality?

200

This number set contains the natural numbers and 0.

What is the set of whole numbers?

200

These segments have equal lengths.

What are congruent segments?

200

The property illustrated by this statement:

(3•5)•2 = 3•(5•2) 

What is the associative property of multiplication?

200
This is always the reason for the first statement in a two-column proof is this.

What is given?

300

This property is illustrated by the following statement

If x + 7 = y, and y = 10, then x + y = 10.

What is the transitive property of equality?

300

This number set contains the whole numbers and their opposites.

What is the set of integers? (Z)

300
Given segment A-B-C, If AB = BC, then B is called this.

What is the midpoint of the segment?

300

The property illustrated by this statement:

3(x + 8) = 3x + 24

What is the distributive property?

300
In a two-column proof, definitions and properties go in this column.

What is the second column?

400

This property states that for real numbers a b and c, if a = b, then a + c = b + c. 

What is the addition property of equality?

400

This number set contains the number pi, and square root of 2, but not fractions or integers such as 2/3 or 5. 

What is the set of irrational numbers?

400

If AB ≅ CD, then AB = CD

What is the definition of congruent segments?

400

This property demonstrates that adding zero to a number does not change the number.

What is the identity property of addition?

400

The statement we are trying to prove goes in this row.

What is the last row?

500
This property states that for real numbers a, b, and c, if a = b, then ac = bc.

What is the multiplication property of equality?

500

This number set contains numbers that can be expressed as a ratio of integers.

What is the set of rational numbers?

500

Because congruence exhibits the reflexive, symmetric, and transitive properties it is this type of relation.

What is an equivalence relation?
500

This property is illustrated by the following statement:

3 • 1/3 = 1

What is the inverse property of multiplication?

500
These are statements that are accepted as true without proof.
What are postulates?
M
e
n
u