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 1 rstu is a rectangle with vertices r(0,0), s(0,a), t(a,a), and u(a,0) 1 given 2 rs = a units 2 ? 3 st = a units 3 distance formula 4 rs ≅ st 4 ? 5 rstu is a square 5 ? 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

Explanation:

Step1: Find length of RS

The points $R(0,0)$ and $S(0,a)$ have the same $x -$coordinate. The distance between two points with the same $x -$coordinate $(x_1,y_1)$ and $(x_1,y_2)$ is given by $|y_2 - y_1|$. Here, $RS=|a - 0|=a$, which is based on the distance - formula concept for vertical lines.

Step2: Justify $RS\cong ST$

Since $RS = a$ and $ST=a$ (from step 1 and given that $ST$ is calculated using distance formula), by the definition of congruence (two segments are congruent if they have the same length), $RS\cong ST$.

Step3: Prove it's a square

A rectangle is a square if two consecutive sides are congruent. Since $RSTU$ is a rectangle and $RS\cong ST$, by the property that if two consecutive sides of a rectangle are congruent, then it's a square, $RSTU$ is a square.

Answer:

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