https://file.aiquickdraw.com/mathbot/file/1727208521741b28g61cb.jpg

This image shows a geometric proof involving line segments on a diagram. You are asked to prove that \( JL = KM \), given that \( JK \cong LM \).

Let's complete the two-column proof, filling in the missing reasons:

### Proof:

| **Statements**                               | **Reasons**                         |
|----------------------------------------------|-------------------------------------|
| 1. \( JK \cong LM \)                         | 1. Given                           |
| 2. \( JK = LM \)                             | 2. Definition of congruent segments |
| 3. \( KL = KL \)                             | 3. Reflexive Property of Equality   |
| 4. \( JK + KL = LM + KL \)                   | 4. Addition Property of Equality    |
| 5. \( JK + KL = JL \), \( LM + KL = KM \)    | 5. Segment Addition Postulate       |
| 6. \( JL = KM \)                             | 6. Substitution                     |

### Explanation:
1. **Given**: \( JK \cong LM \) means the two segments are congruent, hence they are equal in length.
2. **Definition of congruent segments**: \( JK = LM \) because congruent segments have equal lengths.
3. **Reflexive Property**: \( KL = KL \), a segment is equal to itself.
4. **Addition Property**: Adding equal quantities to equal segments gives equal results.
5. **Segment Addition Postulate**: \( JK + KL \) forms \( JL \), and \( LM + KL \) forms \( KM \).
6. **Substitution**: Replacing \( JK + KL \) with \( JL \) and \( LM + KL \) with \( KM \), we get \( JL = KM \).

Would you like further clarification on any part of this proof?

### Related Questions:
1. How do you apply the Segment Addition Postulate in geometry?
2. What is the difference between congruent and equal segments?
3. Why is the Reflexive Property important in geometric proofs?
4. How does the Substitution Property help in algebraic steps of geometric proofs?
5. What are other properties that might be used in congruence and equality proofs?

### Tip:
Always double-check the definitions in proofs—like congruence, equality, and segment properties—to ensure logical flow.

Learn how to prove JL = KM in a geometric diagram where JK ≅ LM. This problem uses congruence, the Segment Addition Postulate, and the Reflexive Property of Equality. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation