For constructing a unique quadrilateral at least __________ measurements are required.

Answer

To construct a unique quadrilateral, we need to determine the minimum number of measurements required. Here’s the step-by-step solution:

### Step 1: Understanding Quadrilaterals
A quadrilateral is a polygon with four sides. To construct a unique quadrilateral, we need to specify certain measurements.

### Step 2: Identifying Measurements
The measurements we can use to define a quadrilateral include:
- The lengths of the sides
- The angles between the sides

### Step 3: Minimum Measurements Required
To construct a unique quadrilateral, we need at least 5 measurements. This can be achieved in the following ways:
1. **Four sides and one angle**: If we know the lengths of all four sides and one angle, we can construct a unique quadrilateral.
2. **Three sides and two included angles**: If we know the lengths of three sides and the measures of the two angles that are included between those sides, we can also construct a unique quadrilateral.

### Conclusion
Thus, the minimum number of measurements required to construct a unique quadrilateral is **5**.

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