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It appears you've uploaded a test from a geometry module. Here’s a breakdown of the first few questions in the document:

1. **Counterexample to Collinear Points**:
   The statement to refute is: "If \( A \), \( B \), and \( C \) are collinear points, then \( AB + BC = AC \)." The correct answer would be a scenario where this condition doesn't hold true. The correct option for this would likely be **D: \( AB > BC \)**.

2. **Relationship between Two Logical Statements**:
   Statement 1: "If a quadrilateral has four right angles, then it is a rectangle."  
   Statement 2: "If a quadrilateral is not a rectangle, then it does not have four right angles."  
   The correct relationship here is that **Statement 2 is the contrapositive of Statement 1**, so the answer is **D**.

3. **Property of Congruence**:
   If \( \overline{AB} \cong \overline{BC} \) and \( \overline{BC} \cong \overline{CD} \), the property showing \( \overline{AB} \cong \overline{CD} \) is the **Transitive Property**, so the answer is **D**.

4. **Solving for \( x \) Given \( QR \cong ST \)**:
   If \( QR = \frac{2}{3}x \) and \( ST = 0.4 \), solve for \( x \):  
   \[
   \frac{2}{3}x = 0.4
   \]  
   Multiply both sides by 3:
   \[
   2x = 1.2
   \]  
   Now divide by 2:
   \[
   x = 0.6
   \]

Do you need further explanation on any of these, or more questions analyzed from the document?

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Here are five related questions that could deepen understanding:

1. How do contrapositive statements differ from inverse statements in logic?
2. Can you provide another example of the transitive property in geometry?
3. What happens when three points are collinear, but \( AB \) is not equal to \( BC \)?
4. What are some other examples of congruent angle proofs?
5. How can we verify that angles in a quadrilateral are congruent?

**Tip**: For proving geometrical statements, always refer to postulates like the Transitive Property or Reflexive Property for clarity.

It appears you've uploaded a test from a geometry module. Here’s a breakdown of the first few questions in the document:

1. Counterexample to Collinear Points: The statement to refute is: "If A, B, and C are collinear points, then AB + BC = AC." The correct answer would be a scenario where this condition doesn't hold true. The correct option for this would likely be D: AB > BC.

2. Relationship between Two Logical Statements: Statement 1: "If a quadrilateral has four right angles, then it is a rectangle."  Statement 2: "If a quadrilateral is not a rectangle, then it does not have four right angles." The correct relationship here is that Statement 2 is the contrapositive of Statement 1, so the answer is D.

3. Property of Congruence: If AB ≅ BC and BC ≅ CD, the property showing AB ≅ CD is the Transitive Property, so the answer is D.

4. Solving for x Given QR ≅ ST: If QR = 2/3 x and ST = 0.4, solve for x: 2/3 x = 0.4 Multiply both sides by 3: 2x = 1.2 Now divide by 2: x = 0.6

Review key geometry concepts including collinear points, congruence properties, and logical relationships between statements. This module covers examples of the Transitive Property, Contrapositive logic, and problem-solving for congruent segments.

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