Question 1-38 Which situation would provide a counterexample to the statement below? You can connect any three points to form a triangle. Three coplanar points. Two points on $$ \overleftrightarrow{A B} $$ and one point not on $$ \stackrel{\leftrightarrow}{A B} $$ Two points not on $$ \stackrel{\leftarrow}{A B} $$ and one point on $$ \overleftrightarrow{A B} $$ Three collinear points.

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To determine a counterexample to the statement **"You can connect any three points to form a triangle,"** we need to identify a scenario where three points **cannot** form a triangle.

### Understanding the Statement:
A triangle is formed by connecting three **non-collinear** points in a plane. If the points are collinear, meaning they all lie on a single straight line, they cannot form a triangle because the "triangle" would essentially collapse into a straight line, lacking area and the distinct sides required.

### Evaluating the Options:

1. **Three Coplanar Points:**
   - **Explanation:** Being coplanar simply means all points lie within the same plane. This does not necessarily prevent the formation of a triangle, as non-collinear coplanar points can form a triangle.
   - **Conclusion:** Not a counterexample.

2. **Two Points on $$ \overleftrightarrow{AB} $$ and One Point Not on $$ \overleftrightarrow{AB} $$:**
   - **Explanation:** Here, two points lie on a line $$ AB $$, and the third point is off that line. These points are **non-collinear**, allowing them to form a triangle.
   - **Conclusion:** Not a counterexample.

3. **Two Points Not on $$ \overleftrightarrow{AB} $$ and One Point on $$ \overleftrightarrow{AB} $$:**
   - **Explanation:** Similar to the previous case, having two points not on line $$ AB $$ and one on it can still allow for a non-collinear arrangement, thus forming a triangle.
   - **Conclusion:** Not a counterexample.

4. **Three Collinear Points:**
   - **Explanation:** All three points lie on the same straight line. As mentioned earlier, this means they cannot form a triangle because they lack the necessary distinct sides.
   - **Conclusion:** **This is a valid counterexample.**

### **Final Answer:**
**Three collinear points.**
Three collinear points cannot form a triangle.

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