Which statement explains how you could use coordinate geometry to prove that quadrilateral abcd is a square?
a. prove that all sides are congruent, and the slopes of consecutive sides are opposite reciprocals
b. prove that segments ad and ab are congruent and parallel
c. prove that opposite sides are congruent and that the slopes of consecutive sides are equal
d. prove the segments bc and cd are congruent and parallel

Option A. is the answer.

Step-by-step explanation:

To prove that a quadrilateral is a square in coordinate geometry we will prove the following properties.

1) We have to prove that all sides of the quadrilateral are equal in length (congruent).

2). Since all the angles of the square always measure 90° therefore, slopes of the consecutive sides should be opposite reciprocals.

Example : ⇒

Therefore, Option A. will be the answer.

The correct answer is option C.

Prove that opposite sides are congruent and that the slopes of consecutive sides are equal

Step-by-step explanation:

Points to remember

Properties of a square

All sides are equal and parallel

All angles are equal and measures 90°

To find the correct option

From the figure we can see a quadrilateral. In order to prove this is a square we have to prove all sides are congruent

The correct answer is option C.

Prove that opposite sides are congruent and that the slopes of consecutive sides are equal

where is the triangle?

f

step-by-step explanation:

f