Which of the following statements is INCORRECT?

Options

A. A unique quadrilateral can be constructed, if the length of its 4 sides and a diagonal is given.
B. A unique quadrilateral can be constructed, if its 2 diagonals and 2 sides are given.
C. A unique quadrilateral can be constructed, if its three sides and its two included angles are given.
D. Both A and C

Answer

To determine which statement is incorrect regarding the construction of quadrilaterals, we need to analyze each option systematically.

### Step-by-Step Solution:

1. **Understand the properties of quadrilaterals**: A quadrilateral is defined by its four sides and can be constructed under certain conditions based on the lengths of its sides and angles.

2. **Evaluate the first statement**:
- "A unique quadrilateral can be constructed if the length of its four sides and a diagonal is given."
- This statement is **correct** because knowing the lengths of all four sides and one diagonal allows for a unique construction of a quadrilateral.

3. **Evaluate the second statement**:
- "A unique quadrilateral can be constructed if two diagonals and two sides are given."
- This statement is also **correct**. Knowing two diagonals and two sides provides enough information to construct a unique quadrilateral.

4. **Evaluate the third statement**:
- "A unique quadrilateral can be constructed if three sides and two included angles are given."
- This statement is **incorrect**. While three sides can define a triangle, adding two angles does not guarantee a unique quadrilateral since the angles could lead to different configurations.

5. **Evaluate the fourth statement**:
- "A unique quadrilateral can be constructed if two adjacent sides and three angles are given."
- This statement is **correct**. Knowing two adjacent sides and the three angles allows for a unique construction of a quadrilateral.

6. **Conclusion**:
- The incorrect statement among the options provided is the third statement: "A unique quadrilateral can be constructed if three sides and two included angles are given."

### Final Answer:
The incorrect statement is: "A unique quadrilateral can be constructed if three sides and two included angles are given."

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