text: # Intermediate Geometry : How to find the length of the diagonal of a parallelogram
  
  ## Example Questions
  
  ### Example Question #1 : How To Find The Length Of The Diagonal Of A Parallelogram
  
  The length of a parallelogram is  cm and the width is  cm. One of its diagonals measures  cm. Find the length of the other diagonal.
  
  Explanation:
  
  The formula for the relationship between diagonals and sides of a parallologram is
  
  ,
  
  where  represents one diagonal,
  
  represents the other diagonal,
  
  represents a side, and
  
  So, in this problem, substitute the known values and solve for the missing diagonal.
  
  So, the missing diagonal is  cm.
  
  ### Example Question #2 : How To Find The Length Of The Diagonal Of A Parallelogram
  
  In the parallogram above, find the length of the labeled diagonal.
  
  Explanation:
  
  In a parallogram, diagonals bisect one another, thus you can set the two segments that are labeled in the picture equal to one another, then solve for .
  
  So,
  
  .
  
  If , then you can substitute 14 into each labeled segment, to get a total of 52.
  
  ### Example Question #3 : How To Find The Length Of The Diagonal Of A Parallelogram
  
  In the parallogram below, find the length of the labeled diagonal.
  
  Explanation:
  
  In a parallelogram, the diagonals bisect one another, so you can set the labeled segments equal to each other and then solve for .
  
  .
  
  If , then you substitute 6 into each labeled segment, to get a total of 40.
  
  ### Example Question #4 : How To Find The Length Of The Diagonal Of A Parallelogram
  
  In the parallelogram above, find the length of the labeled diagonal.
  
  Explanation:
  
  In a parallelogram, the diagonals bisect each other, so you can set the labeled segments equal to one another and then solve for
  
  .
  
  Then, substitute 4.8 for  in each labeled segment to get a total of 11.2 for the diagonal length.
  
  ### Example Question #5 : How To Find The Length Of The Diagonal Of A Parallelogram
  
  Suppose a square has an area of 6.  What is the diagonal of the parallelogram?
  
  Explanation:
  
  Write the formula to find the side of the square given the area.
  
  Find the side.
  
  The diagonal of the square can be solved by using the Pythagorean Theorem.
  
  Substitute and solve for the diagonal, .
  
  ### Example Question #6 : How To Find The Length Of The Diagonal Of A Parallelogram
  
  If the side length of a square is , what is the diagonal of the square?
  
  Explanation:
  
  Write the diagonal formula for a square.
  
  Substitute the side length and reduce.
  
  ### Example Question #7 : How To Find The Length Of The Diagonal Of A Parallelogram
  
  Parallelogram  has diagonals  and  and .
  
  True, false, or undetermined: Parallelogram  is a rectangle.
  
  False
  
  True
  
  Undetermined
  
  False
  
  Explanation:
  
  One characteristic of a rectangle is that its diagonals are congruent. Since the diagonals of Parallelogram  are of different lengths, it cannot be a rectangle.
  
  ### Example Question #8 : How To Find The Length Of The Diagonal Of A Parallelogram
  
  Parallelogram  has diagonals  and  and .
  
  True, false, or undetermined: Parallelogram  is a rhombus.
  
  Undetermined
  
  False
  
  True
explanation: The document is a collection of example questions and answers related to finding the length of the diagonal of a parallelogram. Each example question is followed by a detailed explanation of the solution. The questions cover various scenarios, including finding the length of a diagonal given the sides of the parallelogram, using the property that diagonals bisect each other, and determining properties of special parallelograms like squares and rectangles.
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distilabel_metadata.content: # Intermediate Geometry : How to find the length of the diagonal of a parallelogram
  
  ## Example Questions
  
  ### Example Question #1 : How To Find The Length Of The Diagonal Of A Parallelogram
  
  The length of a parallelogram is  cm and the width is  cm. One of its diagonals measures  cm. Find the length of the other diagonal.
  
  Explanation:
  
  The formula for the relationship between diagonals and sides of a parallologram is
  
  ,
  
  where  represents one diagonal,
  
  represents the other diagonal,
  
  represents a side, and
  
  So, in this problem, substitute the known values and solve for the missing diagonal.
  
  So, the missing diagonal is  cm.
  
  ### Example Question #2 : How To Find The Length Of The Diagonal Of A Parallelogram
  
  In the parallogram above, find the length of the labeled diagonal.
  
  Explanation:
  
  In a parallogram, diagonals bisect one another, thus you can set the two segments that are labeled in the picture equal to one another, then solve for .
  
  So,
  
  .
  
  If , then you can substitute 14 into each labeled segment, to get a total of 52.
  
  ### Example Question #3 : How To Find The Length Of The Diagonal Of A Parallelogram
  
  In the parallogram below, find the length of the labeled diagonal.
  
  Explanation:
  
  In a parallelogram, the diagonals bisect one another, so you can set the labeled segments equal to each other and then solve for .
  
  .
  
  If , then you substitute 6 into each labeled segment, to get a total of 40.
  
  ### Example Question #4 : How To Find The Length Of The Diagonal Of A Parallelogram
  
  In the parallelogram above, find the length of the labeled diagonal.
  
  Explanation:
  
  In a parallelogram, the diagonals bisect each other, so you can set the labeled segments equal to one another and then solve for
  
  .
  
  Then, substitute 4.8 for  in each labeled segment to get a total of 11.2 for the diagonal length.
  
  ### Example Question #5 : How To Find The Length Of The Diagonal Of A Parallelogram
  
  Suppose a square has an area of 6.  What is the diagonal of the parallelogram?
  
  Explanation:
  
  Write the formula to find the side of the square given the area.
  
  Find the side.
  
  The diagonal of the square can be solved by using the Pythagorean Theorem.
  
  Substitute and solve for the diagonal, .
  
  ### Example Question #6 : How To Find The Length Of The Diagonal Of A Parallelogram
  
  If the side length of a square is , what is the diagonal of the square?
  
  Explanation:
  
  Write the diagonal formula for a square.
  
  Substitute the side length and reduce.
  
  ### Example Question #7 : How To Find The Length Of The Diagonal Of A Parallelogram
  
  Parallelogram  has diagonals  and  and .
  
  True, false, or undetermined: Parallelogram  is a rectangle.
  
  False
  
  True
  
  Undetermined
  
  False
  
  Explanation:
  
  One characteristic of a rectangle is that its diagonals are congruent. Since the diagonals of Parallelogram  are of different lengths, it cannot be a rectangle.
  
  ### Example Question #8 : How To Find The Length Of The Diagonal Of A Parallelogram
  
  Parallelogram  has diagonals  and  and .
  
  True, false, or undetermined: Parallelogram  is a rhombus.
  
  Undetermined
  
  False
  
  True
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document is a collection of example questions and answers related to finding the length of the diagonal of a parallelogram. Each example question is followed by a detailed explanation of the solution. The questions cover various scenarios, including finding the length of a diagonal given the sides of the parallelogram, using the property that diagonals bisect each other, and determining properties of special parallelograms like squares and rectangles.
  
  Label: multiple-question-and-answer