Q53. - Algebra 1

Question

Which illustrates the Transitive Property of Equality?

F If $\mathbf{c}=\mathbf{1}$ then $\mathbf{c}\cdot \frac{1}{c}=\mathbf{1}$.

G If $\mathbf{c}=\mathbf{d}$ and $\mathbf{d}=\mathbf{f}$ then $\mathbf{c}=\mathbf{f}$.

H If $\mathbf{c}=\mathbf{d}$ then $\mathbf{d}=\mathbf{c}$.

J If $\mathbf{c}=\mathbf{d}$ and $\mathbf{d}=\mathbf{c}$ then $\mathbf{c}=\mathbf{1}$.

Step-by-Step Solution

Answer

The correct choice is Option G: “If $c=d$ and $d=f$ then $c=f$”

Step 1. State the concept.

According to the Transitive Property of Equality, if a quantity is equal to the second quantity and if the second quantity is equal to a third quantity, then the first quantity is equal to the third quantity.

Step 2. List the given options.

The given options are:

 

F If $c=1,$ then $c\cdot \frac{1}{c}=1$.

G If $c=d$ and $d=f$ then $c=f$.

H If $c=d$ then $d=c$.

J If $c=d$ and $d=c$ then $c=1$.

Step 3. Determine the correct option.

Investigating each option, it is clear that the Option G: “If $c=d$ and $d=f$ then $c=f$” illustrates the transitive property of equality.