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Given: RSTU is a rectangle with vertices [tex]$R(0,0), S(0, a), T(a, a)$[/tex], and [tex]$U(a, 0)$[/tex], where [tex]$a \neq 0$[/tex].
Prove: RSTU is a square.
\begin{tabular}{|c|c|}
\hline Statements & Reasons \\
\hline 1. RSTU is a rectangle with vertices [tex]$R(0,0), S(0, a), T(a, a)$[/tex], and [tex]$U(a, 0)$[/tex] & 1. Given \\
\hline 2. [tex]$RS = a$[/tex] units & 2. Distance formula \\
\hline 3. [tex]$ST = a$[/tex] units & 3. Distance formula \\
\hline 4. [tex]$\overline{RS} \cong \overline{ST}$[/tex] & 4. Definition of congruence \\
\hline 5. RSTU is a square & 5. If two consecutive sides of a rectangle are congruent, then it's a square \\
\hline
\end{tabular}

What is the correct order of reasons that complete the proof?

A. If two consecutive sides of a rectangle are congruent, then it's a square; distance formula; definition of congruence

B. Distance formula; definition of congruence; if two consecutive sides of a rectangle are congruent, then it's a square

C. Distance formula; if two consecutive sides of a rectangle are congruent, then it's a square; definition of congruence

D. Definition of congruence; distance formula; if two consecutive sides of a rectangle are congruent, then it's a square



Answer :

GinnyAnswer
Let's determine the correct order of reasons that complete the proof:

1. Given: RSTU is a rectangle with vertices [tex]\(R(0,0)\)[/tex], [tex]\(S(0, a)\)[/tex], [tex]\(T(a, a)\)[/tex], and [tex]\(U(a, 0)\)[/tex].

2. Prove: RSTU is a square.

We start by providing the statements and necessary reasons to complete the proof.

Statements and Reasons:

1. Statement: [tex]\(RSTU\)[/tex] is a rectangle with vertices [tex]\(R(0, 0)\)[/tex], [tex]\(S(0, a)\)[/tex], [tex]\(T(a, a)\)[/tex], and [tex]\(U(a, 0)\)[/tex].
- Reason: Given.

2. Statement: [tex]\(RS = a\)[/tex] units
- Reason: Distance formula.

3. Statement: [tex]\(ST = a\)[/tex] units
- Reason: Distance formula.

4. Statement: [tex]\(\overline{RS} \cong \overline{ST}\)[/tex]
- Reason: Definition of congruence (Segments with equal length are congruent).

5. Statement: [tex]\(RSTU\)[/tex] is a square.
- Reason: If two consecutive sides of a rectangle are congruent, then it's a square.

Therefore, the correct order of reasons to complete the proof is:

- Distance formula
- If two consecutive sides of a rectangle are congruent, then it's a square
- Definition of congruence

Thus, the correct answer is:

C. distance formula; if two consecutive sides of a rectangle are congruent, then it's a square; definition of congruence

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