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The problem you have uploaded concerns logical statements related to the concept of collinearity of points in geometry. Here's a detailed breakdown of the converse, inverse, and contrapositive of the given statement:

### Original statement:
"If three points lie on the same line, then they are collinear."

### Converse:
The converse of a statement is formed by swapping the hypothesis and the conclusion. In this case, the converse would be:
**"If three points are collinear, then they lie on the same line."**
This is a true statement because collinear points, by definition, lie on the same straight line.

### Inverse:
The inverse is formed by negating both the hypothesis and the conclusion of the original statement. Here, the inverse would be:
**"If three points do not lie on the same line, then they are not collinear."**
This is also true because if points do not lie on the same line, they cannot be collinear by definition.

### Contrapositive:
The contrapositive is formed by swapping the hypothesis and the conclusion and negating both. The contrapositive of the statement would be:
**"If three points are not collinear, then they do not lie on the same line."**
This is also true, and since a contrapositive always has the same truth value as the original statement, this confirms the original statement's validity.

Would you like more details on any of these logical transformations, or have any questions?

Here are five related questions to deepen understanding:
1. What is the definition of collinear points in geometry?
2. How do you differentiate between collinear and non-collinear points geometrically?
3. Why is the contrapositive logically equivalent to the original statement?
4. What other geometric properties can be analyzed using converse, inverse, and contrapositive reasoning?
5. How does the truth value of the inverse relate to that of the original statement?

**Tip:** To easily remember how to form a contrapositive, just swap the parts of the statement (if-then) and negate both sides!

If three points lie on the same line, then they are collinear.

Explore the concept of collinearity in geometry through logical reasoning. This problem involves analyzing the original statement 'If three points lie on the same line, then they are collinear' and its converse, inverse, and contrapositive. Suitable for students in Grades 8-10.

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