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 straigth 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 statement is false, let's analyze each statement one by one:

1. **Statement 1**: A line segment can be produced to any desired length.
- A line segment has two endpoints and can be extended indefinitely in both directions to form a line. Therefore, this statement is **true**.

2. **Statement 2**: Through a given point, only one straight line can be drawn.
- A single point can have infinitely many straight lines passing through it. For example, you can draw a line at any angle from that point. Therefore, this statement is **false**.

3. **Statement 3**: Through two given points, only one straight line can be drawn.
- Given two distinct points, there is exactly one straight line that can connect them. Therefore, this statement is **true**.

4. **Statement 4**: Two straight lines can intersect at one point only.
- Two distinct straight lines can intersect at most at one point. If they intersect at more than one point, they would be the same line. Therefore, this statement is **true**.

Based on the analysis above, the false statement is **Statement 2**.

### Step-by-Step Solution:
1. **Analyze Statement 1**: Determine if a line segment can be extended indefinitely.
- Conclusion: True.

2. **Analyze Statement 2**: Consider how many lines can pass through a single point.
- Conclusion: False.

3. **Analyze Statement 3**: Check if two points can define only one line.
- Conclusion: True.

4. **Analyze Statement 4**: Evaluate the intersection of two lines.
- Conclusion: True.

5. **Identify the false statement**: Based on the evaluations, Statement 2 is false.