# Worksheet: Properties of Equality

In this worksheet, we will practice dealing with the properties of equality and writing an equivalent expression to a given one.

**Q4: **

The diagram shows a rectangular prism (A) that has been divided into three horizontal slices (B) and into four vertical slices (C). The volume of the rectangular prism as represented in (B) is written as , where is the volume of one slice.

Choose an expression for as represented in (C).

- A
- B
- C
- D
- E

What property of multiplication does this diagram show?

- Athe commutative property
- Bthe associative property
- Cthe multiplicative inverse property
- Dthe multiplicative identity property
- Ethe distributive property

How many slices with a volume of 12 volume units are there in the rectangular prism?

- A3
- B
- C
- D4
- E

**Q5: **

Which of the following demonstrates the symmetric property of equality?

- AFor any , .
- BIf , then .
- CIf and , then .

**Q6: **

Which of the following demonstrates the reflexive property of equality?

- AFor any , .
- BIf and , then .
- CIf , then .

**Q7: **

Consider the following equality statements:

- .
- .
- .

Without solving for , , , or , select the true statement.

- A
- B
- C
- D
- E

Without solving for , , , or , select the true statement.

- A
- B
- C
- D
- E

Without solving for , , , or , select the true statement.

- A
- B
- C
- D
- E

Without solving for , , , or , select the true statement.

- A
- B
- C
- D
- E

**Q8: **

Which of the following demonstrates the transitive property of equality?

- AIf and , then .
- BIf , then .
- CFor any , .

**Q9: **

Which of the following figures has an area that can be represented by the expression ?

- A
- B
- C
- D
- E

**Q11: **

Which of the following expressions is equivalent to ?

- A
- B
- C
- D
- E

**Q12: **

Which of the following expressions is equivalent to ?

- A
- B
- C
- D
- E

**Q14: **

Which of the following expressions is equivalent to ?

- A
- B
- C
- D
- E

**Q15: **

Determine the value of that makes the equation true for all values of .

**Q16: **

Determine the value of that makes the equation true for all values of .

**Q17: **

Determine the value of that makes the equation true for all values of .