Question

what geometric reason justifies the transition from statement 6 to statement 7? transitive property substitution subtraction property of equality multiplication property of equality

Explanation:

To determine the geometric reason for the transition from statement 6 to 7, we analyze the options:

• Transitive Property: If \(a = b\) and \(b = c\), then \(a = c\). But this is about equality between three quantities, not a direct substitution or operation on an equation.
• Substitution: If we know the value of one variable (or expression) and substitute it into another equation, this is substitution. For example, if \(x = 5\) and we have an equation with \(x\), we substitute \(5\) for \(x\). This is a common geometric reasoning when replacing a known value or expression.
• Subtraction Property of Equality: States that if \(a = b\), then \(a - c = b - c\). This is about subtracting the same quantity from both sides of an equation, not about substituting a value.
• Multiplication Property of Equality: States that if \(a = b\), then \(a\times c = b\times c\). This is about multiplying both sides by the same quantity, not about substitution.

Since the transition from statement 6 to 7 likely involves replacing a known value or expression with its equivalent (e.g., substituting a length or angle measure), the correct reason is Substitution.

Answer:

B. Substitution