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The problem shown involves determining whether there is enough information to conclude that line \( h \) is perpendicular to line \( j \), and which theorem among Theorem 3-1, 3-2, 3-3, or 3-4 supports this conclusion.

### Analyzing the Diagram:
- The angle between lines \( h \) and \( j \) is labeled as \( 90^\circ \), which typically indicates perpendicularity.
- The labels \( 12 \) and \( 13 \) next to the angle imply two segments adjacent to the right angle, likely suggesting some equality or relationship that is used in a specific theorem.

### Possible Theorems:
While I don’t have the exact statements of Theorem 3-1 through 3-4, common geometric theorems that would apply include:
- **Perpendicularity Theorem**: If two lines form a right angle (as labeled by a \( 90^\circ \) symbol), they are perpendicular.
- **Theorem on Congruent Segments**: Could involve confirming perpendicularity using properties such as congruent adjacent segments or sides.

Based on typical naming:
- **Theorem 3-1** might relate to a general perpendicularity test.
- **Theorem 3-2** could relate to properties of angles formed between intersecting lines.
- **Theorem 3-3** might involve congruent segments or triangles.
- **Theorem 3-4** often involves properties about the converse of perpendicular or angle theorems.

Given the angle is \( 90^\circ \), **Theorem 3-2** (Yes, Theorem 3-2) seems likely if it directly involves perpendicular lines. This could confirm that \( h \perp j \) by the presence of the right angle.

Would you like a deeper explanation or have any specific questions about perpendicularity or related theorems?

### Questions for Further Exploration:
1. What are the exact statements of Theorems 3-1 to 3-4, and how do they differ?
2. Can perpendicularity be determined without directly using a \( 90^\circ \) angle?
3. How would congruent segments impact the decision if the angle were not labeled?
4. What other scenarios would Theorem 3-3 or 3-4 apply to this configuration?
5. Why is a \( 90^\circ \) angle essential in proving perpendicularity?

#### Tip:
When working with diagrams, ensure you verify angle measures directly on the diagram to support your conclusions.

Determine whether enough info is given to conclude that line h is perpendicular to line j. Provide the theorem (Theorem 3-1, 3-2, 3-3, or 3-4) that supports your conclusion.

Learn how to determine if there is enough information to conclude that line h is perpendicular to line j by applying Theorems 3-1, 3-2, 3-3, or 3-4. This problem covers key geometric concepts related to perpendicularity and angle relationships, suitable for students in Grades 8-10.

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