In parallelogram pqsr what is pq

General
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in parallelogram pqsr what is pq

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In parallelogram PQSR, what is PQ?

In a parallelogram, opposite sides are equal in length. Therefore, if we have a parallelogram PQSR, we can deduce the following:

  1. Opposite Sides Are Equal: In PQSR, side PQ will be equal to side SR, and side PS will be equal to side QR.

  2. Vector Nature: If we consider vector representation, the vector \overrightarrow{PQ} will be equal in magnitude and direction but opposite in sense to \overrightarrow{SR}, meaning \overrightarrow{PQ} = - \overrightarrow{SR}.

To determine the exact length of PQ, you would need either:

  • The Length of One of the Opposite Sides: The problem could potentially provide the length of SR, which will be equal to PQ.
  • Coordinate Geometry: If you have the coordinates of points P, Q, S, and R, you can calculate the distance between P and Q using the distance formula:
    PQ = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
  1. Given Values: Often in problems, specific values or relationships between the sides are provided to find the exact length. For example, if SR (opposite side) length is given, that length directly tells you PQ.

Example Calculation:

If we are given coordinates for points P and Q:

  • Point P has coordinates (x1, y1)
  • Point Q has coordinates (x2, y2)

Then the length of PQ can be calculated as:

PQ = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}

In Summary:

To determine the length of PQ in the parallelogram PQSR:

  1. Identify the length of the opposite side (SR).
  2. Use the Euclidean distance formula if coordinates are given.
  3. Apply properties of parallelograms where PQ is equal to SR.

If any specific values or additional details were given, the exact numeric value of PQ can be determined accordingly.