Answer :
To prove that [tex]\( RSTU \)[/tex] is a square, we need to follow logical steps with accurate justifications for each statement. Below is the solution outlined step-by-step with the correct order of reasons:
1. Statements and Reasons:
[tex]\[ \begin{array}{|l|l|} \hline \multicolumn{1}{|c|}{\text{Statements}} & \multicolumn{1}{c|}{\text{Reasons}} \\ \hline 1. \, RSTU \, \text{is a rectangle with vertices} \, R (0,0), S (0, a ), T ( a , a ), & 1. \, \text{given} \\ U \, ( a , 0) & \\ \hline 2. \, RS = a \, \text{units} & 2. \, \text{distance formula} \\ \hline 3. \, ST = a \, \text{units} & 3. \, \text{distance formula} \\ \hline 4. \, \overline{RS} \cong \overline{ST} & 4. \, \text{definition of congruence} \\ \hline 5. \, RSTU \, \text{is a square} & 5. \, \text{If two consecutive sides of a rectangle are congruent, then it's a square} \\ \hline \end{array} \][/tex]
Now we can identify the correct order of reasons to complete the proof from the given options:
2. [tex]\( \text{distance formula} \)[/tex]
3. [tex]\( \text{distance formula} \)[/tex]
4. [tex]\( \text{definition of congruence} \)[/tex]
5. [tex]\( \text{If two consecutive sides of a rectangle are congruent, then it's a square} \)[/tex]
Thus, the correct answer is:
C. distance formula; definition of congruence; if two consecutive sides of a rectangle are congruent, then it's a square
1. Statements and Reasons:
[tex]\[ \begin{array}{|l|l|} \hline \multicolumn{1}{|c|}{\text{Statements}} & \multicolumn{1}{c|}{\text{Reasons}} \\ \hline 1. \, RSTU \, \text{is a rectangle with vertices} \, R (0,0), S (0, a ), T ( a , a ), & 1. \, \text{given} \\ U \, ( a , 0) & \\ \hline 2. \, RS = a \, \text{units} & 2. \, \text{distance formula} \\ \hline 3. \, ST = a \, \text{units} & 3. \, \text{distance formula} \\ \hline 4. \, \overline{RS} \cong \overline{ST} & 4. \, \text{definition of congruence} \\ \hline 5. \, RSTU \, \text{is a square} & 5. \, \text{If two consecutive sides of a rectangle are congruent, then it's a square} \\ \hline \end{array} \][/tex]
Now we can identify the correct order of reasons to complete the proof from the given options:
2. [tex]\( \text{distance formula} \)[/tex]
3. [tex]\( \text{distance formula} \)[/tex]
4. [tex]\( \text{definition of congruence} \)[/tex]
5. [tex]\( \text{If two consecutive sides of a rectangle are congruent, then it's a square} \)[/tex]
Thus, the correct answer is:
C. distance formula; definition of congruence; if two consecutive sides of a rectangle are congruent, then it's a square
