Question

post test: polygons
1 rstu is a rectangle with vertices r(0,0), s(0,a), t(a,a), and u(a,0)
2 rs = a units
3 st = a units
4 rs ≅ st
5 rstu is a square
what is the correct order of reasons that complete the proof?
a. if two consecutive sides of a rectangle are congruent, then its a square; distance formula; definition of congruence
b. definition of congruence; distance formula; if two consecutive sides of a rectangle are congruent, then its a square
c. distance formula; if two consecutive sides of a rectangle are congruent, then its a square; definition of congruence
d. distance formula; definition of congruence; if two consecutive sides of a rectangle are congruent, then its a square

Explanation:

We first use the distance formula to find the lengths of sides RS and ST. Then, we use the definition of congruence to show $\overline{RS}\cong\overline{ST}$. Finally, we use the fact that if two - consecutive sides of a rectangle are congruent, then it's a square.

Answer:

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