https://file.aiquickdraw.com/mathbot/file/1727369718712ack9jam6.jpg

Let's analyze the image and solve the proof.

### Given Information:
- \( JK \cong LM \) (Given).

### Prove:
- \( JL = KM \).

### Proof Table:
| Statements             | Reasons                          |
|------------------------|----------------------------------|
| 1. \( JK \cong LM \)    | 1. Given                         |
| 2. \( JK = LM \)        | 2. Definition of Congruence      |
| 3. \( KL = KL \)        | 3. Reflexive Property            |
| 4. \( JK + KL = LM + KL \) | 4. Segment Addition Postulate   |
| 5. \( JK + KL = JL \) and \( LM + KL = KM \) | 5. Segment Addition Postulate   |
| 6. \( JL = KM \)        | 6. Transitive Property of Equality |

### Correct Reasons:
- **1. Given**
- **3. Transitive Property**
- **5. Segment Addition Postulate**

The correct reasons that complete the proof are:
- Given
- Transitive Property
- Segment Addition Postulate

Would you like further details or any clarifications?

Here are five related questions for further exploration:
1. What is the Segment Addition Postulate?
2. How does the Transitive Property apply in geometry?
3. Can the Pythagorean Theorem be used for line segments in any proof?
4. Why is the Reflexive Property necessary for proofs involving equal segments?
5. How does the definition of congruence relate to equality in geometric proofs?

**Tip**: In geometric proofs, always consider the congruence and equality relationships separately at first before combining them through properties like transitivity or addition.

In the diagram, JK ≅ LM. Prove: JL = KM. Which reasons correctly complete the proof for the given statement numbers?

Explore the geometric proof involving congruent segments JK ≅ LM. The proof uses key geometry concepts such as the Segment Addition Postulate, Reflexive Property, and Transitive Property to prove JL = KM. Suitable for high school students, Grades 9-11.

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