Question

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

Answer 1

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

Step-by-step 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\\e0 \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