Question

Can someone help me figure out this geometry question I’m confused?

Answer 1

Answer:

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

Explanation:

Given that RSTU is a rectangle with vertices;

$\begin{gathered} R(0,0),S(0,a),T(a,a)\text{ and U(a,0)} \\ a\ne0 \end{gathered}$

So, using the distance formula;

$RS=a\text{ units}$

Reason; distance formula

$ST=a\text{ units}$

Since both side RS and ST have the same length, then;

$RS\cong ST$

Reason: definition of congruence

So, since two consecutive sides of a rectangle are congruent then;

$\text{RSTU is a Square}$

Reason: if two consecutive sides of a rectangle are congruent, then it's a square