https://file.aiquickdraw.com/mathbot/file/1727054701746mdsxha86.jpg

Let's work through this proof step by step.

### Given:
- \( SU \cong LR \)
- \( TU \cong LN \)

### To Prove:
- \( ST \cong NR \)

### Steps for the Proof:
You have the following steps listed in the image. Let's fill in the reasoning and complete the missing statements.

#### a. \( SU \cong LR \), \( TU \cong LN \)  
**Reason**: Given.

#### b. \( SU + TU = ST \), \( LR + LN = NR \)  
**Reason**: Definition of congruent segments (Segment Addition Postulate).

#### c. \( SU = ST + TU \)  
\( LR = LN + NR \)  
**Reason**: Property of equality.

#### d. \( ST + TU = LN + NR \)  
**Reason**: Substitution (replace congruent parts with equal expressions).

#### e. \( ST + LN = LN + NR \)  
**Reason**: Substitution property.

#### f. \( ST = NR \)  
**Reason**: Subtraction Property of Equality (canceling out the same term on both sides).

#### g. \( ST \cong NR \)  
**Reason**: Definition of congruence (equal lengths lead to congruent segments).

This completes the proof.

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Would you like more details on any step? Here are 5 related questions for practice:

1. What is the Segment Addition Postulate?
2. How do you apply substitution in geometric proofs?
3. Why is the definition of congruent segments important in geometry proofs?
4. What is the subtraction property of equality, and when is it used?
5. How does defining congruence help in proving equal segment lengths?

**Tip**: Always make sure to reference both definitions and postulates in proofs to keep the reasoning clear.

Given that SU ≅ LR and TU ≅ LN, prove that ST ≅ NR. Complete the proof with proper reasons and statements.

Learn how to prove that ST is congruent to NR given SU ≅ LR and TU ≅ LN, using the Segment Addition Postulate, substitution, and subtraction property of equality. This problem is suitable for high school geometry students.

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