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Construction of Parallelogram When Both the Diagonals and the Angle between Them Are Given Are Given.

To construct ...

Question

To construct a parallelogram given its length of diagonals, which of the following additional information is required?

One angle of the parallelogram

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Two angles of the parallelogram

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The angle between the diagonals

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None of the above

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Solution

The correct option is C
The angle between the diagonals

We know diagonals of a parallelogram bisect each other. As we are given the length of the diagonals, we can draw unique set of diagoanls if the angle between them are given.

Therefore, if we know $∠ A O D$ we can construct the diagonals and join the 4 end points to form a paralellogram.

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