Here’s a breakdown of the problem:

You are asked to match each statement with the correct mathematical property. The four properties listed are:

1. Subtraction Property of Equality
2. Substitution
3. Reflexive Property of Equality
4. Transitive Property of Equality

Let’s look at each statement:

1. If $x = y$ and $y = z$, then $x = z$: This demonstrates the Transitive Property of Equality, which states that if one quantity equals a second, and the second equals a third, then the first equals the third.

2. $A = A$: This is an example of the Reflexive Property of Equality, which states that any quantity is equal to itself.

3. If $a = b$, then $a - c = b - c$: This shows the Subtraction Property of Equality, where subtracting the same number from both sides of an equation keeps the equation balanced.

4. If $x = 1$, then $2x - 5 = 2(1) - 5$: This is an example of Substitution, as the value of $x = 1$ is substituted into the equation.

Therefore, the correct matches are:

• Transitive Property of Equality: If $x = y$ and $y = z$, then $x = z$
• Reflexive Property of Equality: $A = A$
• Subtraction Property of Equality: If $a = b$, then $a - c = b - c$
• Substitution: If $x = 1$, then $2x - 5 = 2(1) - 5$

Do you want further details or have any questions about this?

Here are 5 related questions for deeper understanding:

1. Can you explain the Associative Property and how it differs from the Transitive Property?
2. How does the Addition Property of Equality work compared to the Subtraction Property of Equality?
3. Could you provide an example of the Reflexive Property using inequalities?
4. How is the Substitution Property applied in solving systems of equations?
5. What is the Symmetric Property of Equality, and how does it relate to the Reflexive and Transitive properties?

Tip: Understanding the properties of equality is essential for solving equations consistently, especially when manipulating algebraic expressions!