Ask a New Question
Menu

Prove that the following vertices form a parallelogram by showing that the opposite sides are parallel.

(1 point)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
The slope of SA is
Response area
The slope of AN is
Response area
The slope of ND is
Response area
The slope of DS is
Response area
Is this a parallelogram?
Response area
. I know this because the opposite sides of the quadrilateral are parallel.
Yes
m=−
5
8
m=−58No
m=
5
8
m=58
m=
6
5
m=65
m=−
6
5
m=−65

1 answer

To prove that the quadrilateral formed by the vertices S, A, N, and D is a parallelogram, we will show that the opposite sides are parallel by calculating their slopes.

  1. Calculate the slopes of the sides:

    • Slope of SA: \( \text{slope} = m_{SA} = -\frac{5}{8} \)

    • Slope of AN: \( \text{slope} = m_{AN} = \frac{5}{8} \)

    • Slope of ND: \( \text{slope} = m_{ND} = \frac{6}{5} \)

    • Slope of DS: \( \text{slope} = m_{DS} = -\frac{6}{5} \)

  2. Determine if opposite sides are parallel:

    • The slopes of sides SA and AN:

      • \( m_{SA} = -\frac{5}{8} \)
      • \( m_{ND} = \frac{6}{5} \) (not equal)

    • The slopes of sides ND and DS:

      • \( m_{ND} = \frac{6}{5} \)
      • \( m_{DS} = -\frac{6}{5} \) (not equal)

  3. Determine if the opposite sides' slopes are equal:

    • Compare SA and ND:
      • \( m_{SA} = -\frac{5}{8} \) and \( m_{ND} = \frac{6}{5} \) (not parallel).
    • Compare AN and DS:
      • \( m_{AN} = \frac{5}{8} \) and \( m_{DS} = -\frac{6}{5} \) (not parallel).

Since neither pair of opposing slopes are equal, the solution leads us to conclude that the opposite sides are not parallel.

So, the answers you need to provide in your response areas are:

  • The slope of SA is: \( -\frac{5}{8} \)
  • The slope of AN is: \( \frac{5}{8} \)
  • The slope of ND is: \( \frac{6}{5} \)
  • The slope of DS is: \( -\frac{6}{5} \)
  • Is this a parallelogram? No

And the reasoning is: I know this because the opposite sides of the quadrilateral are not parallel.