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I have displayed the image you uploaded. Now, I will help you solve the questions based on the geometric properties of congruence, equality, or definitions. Let's go through them one by one:

1. **If \( PQ = PQ \), then \( \overline{PQ} \cong \overline{PQ} \)**: Reflexive Property of Congruence.

2. **If \( K \) is between \( J \) and \( L \), then \( JK + KL = JL \)**: Segment Addition Postulate.

3. **\( \overline{EF} \cong \overline{EF} \)**: Reflexive Property of Congruence.

4. **If \( RS = TU \), then \( RS + XY = TU + XY \)**: Addition Property of Equality.

5. **If \( AB = DE \), then \( DE = AB \)**: Symmetric Property of Equality.

6. **If \( Y \) is the midpoint of \( \overline{XZ} \), then \( XY = YZ \)**: Definition of a Midpoint.

7. **If \( \overline{FG} \cong \overline{HI} \) and \( \overline{HI} \cong \overline{JK} \), then \( \overline{FG} \cong \overline{JK} \)**: Transitive Property of Congruence.

8. **If \( AB + CD = EF + CD \), then \( AB = EF \)**: Subtraction Property of Equality.

9. **If \( PQ + RS = TV \) and \( RS = WX \), then \( PQ + WX = TV \)**: Substitution Property of Equality.

10. **If \( LP = PN \), and \( L, P, \) and \( N \) are collinear, then \( P \) is the midpoint of \( \overline{LN} \)**: Definition of a Midpoint.

11. **If \( \overline{UV} \cong \overline{UV} \), then \( UV = UV \)**: Reflexive Property of Equality.

12. **If \( CD + DE = CE \), then \( CD = CE - DE \)**: Subtraction Property of Equality.

13. **If \( 2XY = XZ \), then \( XY = \frac{1}{2}XZ \)**: Division Property of Equality.

14. **If \( RS = ST \) and \( ST = 2UV \), then \( RS = 2UV \)**: Transitive Property of Equality.

Would you like more details on any of these properties or have any questions?

Here are 5 related questions to deepen your understanding:
1. What is the difference between the Transitive and Symmetric Properties of Equality?
2. How does the Segment Addition Postulate work in geometric proofs?
3. Can you explain the Reflexive Property and how it applies to both equality and congruence?
4. How can the Substitution Property simplify solving equations in geometry?
5. What role does the definition of a midpoint play in proofs involving line segments?

**Tip**: Understanding the properties of equality and congruence is key to writing clear and correct geometric proofs!

Justify each statement using a property of equality, property of congruence, definition, or postulate.

Solve and justify geometric statements using properties of congruence and equality. Explore the Reflexive, Transitive, and Symmetric Properties as well as the definition of a midpoint and the Segment Addition Postulate. Suitable for students in Grades 7-10.

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