Which of the following statements is false?

Options

A. A line segment can be produced to any desired length
B. Through a given point only one straight line can be drawn
C. Through two given points, it is possible to draw one and only one straight line
D. Two straight lines can intersect at one point only

Answer

To determine which of the following statements is false, we will evaluate each statement one by one.

1. **Statement 1**: A line segment can be produced to any desired length.
- This statement is **true**. A line segment can indeed be extended indefinitely in both directions to form a line.

2. **Statement 2**: Through a given point, only one straight line can be drawn.
- This statement is **false**. Through a given point, an infinite number of straight lines can be drawn in different directions.

3. **Statement 3**: Through two given points, it is possible to draw one straight line.
- This statement is **true**. There is exactly one straight line that can be drawn through any two distinct points.

4. **Statement 4**: Two straight lines can intersect at any point.
- This statement is **true**. Two straight lines can intersect at one point unless they are parallel.

After evaluating all the statements, we find that the false statement is:

**Conclusion**: Through a given point, only one straight line can be drawn (Statement 2) is the false statement.