Question

Which of the following statement is/are correct?
We can construct a quadrilateral:

• A. when its opposite sides are given
• B. when its four angles and a side are given
• C. when its diagonals are given
• D. when its three angles and any two adjacent sides are given

Answer 1

The correct option is D when its three angles and any two adjacent sides are given

To construct a unique quadrilateral, we will need a minimum of $5$ dimensions.

Here in option A, only four dimensions are provided, so a unique quadrilateral not possible because we don't know its angles.

In option B, we have five dimensions, but it does not result in a unique quadrilateral. we needed one more side length to construct uniquely.

In option C, It is not possible to construct a unique quadrilateral from only two diagonals given, unless it is a rhombus or square.

In option D, we have five dimensions. Here if we draw a side first then mark the angle on both ends then we can construct a quadrilateral uniquely.

Hence option D is correct.