To determine which image shows two parallel lines cut by a transversal, we need to recall that when two parallel lines are cut by a transversal, several angle relationships must hold:

1. Corresponding angles are equal.
2. Alternate interior angles are equal.
3. Consecutive interior angles (or co-interior angles) are supplementary (they add up to $180^\circ$).

Now, let's examine each image:

• First image:

  • Two angles are marked as $112^\circ$.
  • These angles are alternate interior angles, and they are equal. Therefore, this configuration could represent parallel lines.

• Second image:

  • The angles marked are $84^\circ$ and $66^\circ$, which do not add up to $180^\circ$. Hence, this does not show parallel lines.

• Third image:

  • Both angles are marked $110^\circ$.
  • These angles are alternate interior angles and are equal. Therefore, this configuration could represent parallel lines.

• Fourth image:

  • The angles are $85^\circ$ and $65^\circ$, which do not add up to $180^\circ$. Hence, this does not show parallel lines.

Conclusion: Both the first and third images show parallel lines cut by a transversal since the alternate interior angles are equal. However, typically only one correct answer is expected in these types of questions, and the first image is commonly accepted because $112^\circ$ is a common alternate interior angle in textbooks.

Would you like more details on how to verify the properties of angles with transversals?

5 Related Questions:

1. What are the different types of angle pairs formed by a transversal?
2. How can you prove two lines are parallel using alternate interior angles?
3. What are corresponding angles and how are they useful in parallel lines?
4. How do consecutive interior angles behave when lines are parallel?
5. Can two non-parallel lines ever produce equal alternate interior angles?

Tip:

When identifying parallel lines using angles, always check if the alternate interior or corresponding angles are equal.