Ask a New Question
Menu

The points R (0,1), I(2,−2), C(3,1)

, and O(1,4)
are the vertices of a quadrilateral. Is RICO
is a parallelogram? How do you know? (Select all that apply)(2 points)
Responses

No, RICO
is not a parallelogram.
No, cap r cap i cap c cap o is not a parallelogram.

Yes. I found the slopes of RI
and CO
and found that they had the same slope. I then found the slopes of IC
and OR
and they also had the same slope. Since they have same slopes, it means that the opposite sides are parallel to each other. This proves that RICO
is a parallelogram.
Yes. I found the slopes of cap r cap iand cap c cap o and found that they had the same slope. I then found the slopes of cap i cap cand cap o cap rand they also had the same slope. Since they have same slopes, it means that the opposite sides are parallel to each other. This proves that cap r cap i cap c cap o is a parallelogram.

Yes. I found the midpoint of the diagonals. They met at the same point so it means we have diagonals that are bisected. This means this is a parallelogram.
Yes. I found the midpoint of the diagonals. They met at the same point so it means we have diagonals that are bisected. This means this is a parallelogram.

Yes. I found the slopes of RI
and OR
and found that they had the same slope. I then found the slopes of IC
and CO
and they also had the same slope. Since they have same slopes, it means that the opposite sides are parallel to each other. This proves that RICO
is a parallelogram.
Yes. I found the slopes of cap r cap iand cap o cap rand found that they had the same slope. I then found the slopes of cap i cap cand cap c cap o and they also had the same slope. Since they have same slopes, it means that the opposite sides are parallel to each other. This proves that cap r cap i cap c cap o is a parallelogram.

Yes. I found the distance of RI
and CO
and found that they are the same distance. I then found the distance of IC
and OR
and they are also the same distance. Since they are the same distance, it means that the opposite sides are congruent to each other. This proves that RICO
is a parallelogram.
Yes. I found the distance of cap r cap iand cap c cap o and found that they are the same distance. I then found the distance of cap i cap cand cap o cap rand they are also the same distance. Since they are the same distance, it means that the opposite sides are congruent to each other. This proves that cap r cap i cap c cap o is a parallelogram.

Yes. I found the slope of IC
and OR
and the distance of IC
and OR
. I found that the slopes were the same which means that IC
and OR
are parallel and IC
and OR
are the same length. This allows me to prove that this forms a parallelogram

1 answer

To determine whether the quadrilateral RICO is a parallelogram, we can use several properties. Let's analyze the options provided:

  1. Using slopes to determine parallel sides:

    • If two pairs of opposite sides have the same slopes, they are parallel, which is a characteristic of parallelograms.

  2. Using midpoints of diagonals:

    • If the midpoints of the diagonals are the same, this indicates that the diagonals bisect each other, which is another condition for a parallelogram.

  3. Using distances to check for congruent sides:

    • If two pairs of opposite sides are equal in length, that also indicates that the figure is a parallelogram.

Based on these criteria, the correct responses that justify whether RICO is a parallelogram include:

  • Yes. I found the slopes of RI and CO and found that they had the same slope. I then found the slopes of IC and OR and they also had the same slope. Since they have the same slopes, it means that the opposite sides are parallel to each other. This proves that RICO is a parallelogram.

  • Yes. I found the midpoint of the diagonals. They met at the same point so it means we have diagonals that are bisected. This means this is a parallelogram.

  • Yes. I found the distance of RI and CO and found that they are the same distance. I then found the distance of IC and OR and they are also the same distance. Since they are the same distance, it means that the opposite sides are congruent to each other. This proves that RICO is a parallelogram.

You would select any of these options, as they correctly justify the conclusion that RICO is a parallelogram using various properties.