Question

select the correct answer.
given: rstu is a rectangle with vertices r(0,0), s(0,a), t(a,a), and u(a,0), where a ≠ 0.
prove: rstu is a square.

statements	reasons
2. rs = a units	2.?
3. st = a units	3. distance formula
4. \\(\overline{rs} \cong \overline{st}\\)	4.?
5. rstu is a square.	5.?

what is the correct order of reasons that complete the proof?
a. distance formula; if two consecutive sides of a rectangle are congruent, then its a square; definition of congruence
b. definition of congruence; distance formula; if two consecutive sides of a rectangle are congruent, then its a square
c. if two consecutive sides of a rectangle are congruent, then its a square; distance formula; definition of congruence
d. distance formula; definition of congruence; if two consecutive sides of a rectangle are congruent, then its a square

Explanation:

1. For step 2, calculating the length of $\overline{RS}$ uses the distance formula between points $R(0,0)$ and $S(0,a)$.
2. For step 4, stating $\overline{RS} \cong \overline{ST}$ follows the definition of congruent segments (segments of equal length are congruent).
3. For step 5, concluding RSTU is a square uses the theorem: if two consecutive sides of a rectangle are congruent, then it is a square.

Answer:

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