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:

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 $a \parallel b$.

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.

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 $AB \parallel DC$.

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.

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?

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.