https://file.aiquickdraw.com/mathbot/file/1734544303974h544mvsx.jpg

To determine which lines are parallel in the diagrams, we rely on **parallelism criteria** such as **alternate interior angles**, **corresponding angles**, or **co-interior angles (supplementary angles)**. Let’s analyze each figure:

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### 1. Diagram **а**:  
- Lines \( a \) and \( b \) are cut by transversal \( c \).  
- The angles given are \( 113^\circ \) and \( 67^\circ \).  
- Since \( 113^\circ + 67^\circ = 180^\circ \), the angles are **supplementary**.  
- **Criterion**: Co-interior angles sum to \( 180^\circ \).  
- **Conclusion**: Lines \( a \parallel b \).

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### 2. Diagram **б**:  
- Lines \( a \) and \( b \) are intersected by transversal \( c \).  
- The angles \( 118^\circ \) and \( 52^\circ \) are provided.  
- \( 118^\circ + 52^\circ = 170^\circ \), which is **not equal to 180^\circ**.  
- **Conclusion**: Lines \( a \) and \( b \) are **not parallel**.

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### 3. Diagram **в**:  
- Quadrilateral \( ABCD \) is given.  
- The angles \( \angle A = 50^\circ \), \( \angle D = 50^\circ \), and \( \angle C = 130^\circ \).  
- Since \( \angle A = \angle D \), and opposite angles in a parallelogram are equal, sides \( AB \) and \( DC \) are **parallel**.  
- **Criterion**: Equal corresponding angles or properties of a parallelogram.  
- **Conclusion**: Lines \( AB \parallel DC \).

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### 4. Diagram **г**:  
- Triangle-like shape \( ABCDE \) includes a right angle at \( B \) and perpendiculars \( AB \) and \( DE \).  
- No explicit angles or corresponding conditions suggest parallelism.  
- **Conclusion**: No clear parallel lines are identified.

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### Final Answer:
- In **diagram а**: \( a \parallel b \) (co-interior angles sum to \( 180^\circ \)).  
- In **diagram в**: \( AB \parallel DC \) (properties of a parallelogram).

Would you like a step-by-step explanation for any specific diagram?

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### Related Questions:
1. What are the conditions for two lines to be parallel?  
2. How do alternate interior angles help identify parallel lines?  
3. Can a quadrilateral always guarantee parallel sides?  
4. How do we prove parallelism using transversal angles?  
5. Why is \( 180^\circ \) significant in parallel line criteria?

**Tip**: Always look for supplementary or congruent angles when identifying parallel lines.

Find the parallel lines in the diagrams and indicate the criterion for parallelism.

Learn how to determine parallel lines in geometric diagrams using angle relationships like co-interior angles, alternate interior angles, and corresponding angles. This problem is suitable for students in Grades 8-10, covering fundamental geometry concepts and proofs.

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