Is the following shape a square? how do you know? ​

no, because the sides are not congruent

 The correct option is (C). Yes, the opposite sides are parallel, and all sides are the same length.

Step-by-step explanation:  We are given to check whether the shape in the figure is a square or not.

From the figure, we note that the co-ordinates of the vertices of shape ABCD are A(-1, 2), B(-3, 0), C(-1, -2) and D(1, 0).

The lengths of the sides of ABCD are calculated by distance formula as follows:

So, the lengths of all the sides are equal.

We know that the slopes of two parallel lines are equal and slopes of two perpendicular lines have product - 1.  

Now, the slopes of the sides of ABCD are given by

Therefore, we have

m = o, n = p, m × n = n × o = o × p = p × m = -1,

which implies that the opposite sides are parallel and adjacent sides are perpendicular.

So, ABCD is a square.

Thus, (C) is the correct option.

 The correct option is (C). Yes, the opposite sides are parallel, and all sides are the same length.

Step-by-step explanation:  We are given to check whether the shape in the figure is a square or not.

From the figure, we note that the co-ordinates of the vertices of shape ABCD are A(-1, 2), B(-3, 0), C(-1, -2) and D(1, 0).

The lengths of the sides of ABCD are calculated by distance formula as follows:

So, the lengths of all the sides are equal.

We know that the slopes of two parallel lines are equal and slopes of two perpendicular lines have product - 1.  

Now, the slopes of the sides of ABCD are given by

Therefore, we have

m = o, n = p, m × n = n × o = o × p = p × m = -1,

which implies that the opposite sides are parallel and adjacent sides are perpendicular.

So, ABCD is a square.

Thus, (C) is the correct option.

a

yes , the opposite sides are parallel and all sides are the same length

Step-by-step explanation:

B

Step-by-step explanation:

it is a rectangle. each opposite sides ARE parallel but not every side is equal like a square so B

C. Yes the opposite sides are parallel and all sides are the same length.

Step-by-step explanation:

Hello! The answer is C. A square is, "a plane figure with four equal straight sides and four right angles." Looking at the shape, it matches the definition. Therefore, C. Have an awesome day! :)

No. It is not a square. Clearly this quadrilateral does not match all of the critera needed to fit the image/idea of a square. Although all of the vertices are 90 degree angles and the polygon is indeed a quadrilateral, the sides of the figure are not all the same length. That image is not one of squarish preportions. Therfore, it is not a square.

P.S. I tried to add in mathmatic words. Im not that much of a knowitall. Hope they get u an A+!!!