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The problem asks to determine which lines are parallel if ∠3 and ∠5 are congruent, and the diagram shows two transversal lines crossing a set of four lines labeled *a*, *b*, *c*, and *d*. 

Given that ∠3 and ∠5 are congruent, they are **corresponding angles** formed by a transversal cutting through two parallel lines. According to the **corresponding angles postulate**, if two lines are cut by a transversal and the corresponding angles are congruent, then the two lines must be parallel.

Here, lines *c* and *d* are cut by the transversal, and angles 3 and 5 are corresponding angles. Therefore, lines *c* and *d* must be parallel.

Thus, the correct answer is **A) c // d**.

Would you like further explanation or more details? 

Here are 5 related questions you might want to explore:
1. What are alternate interior angles and how do they relate to parallel lines?
2. How do you prove that two lines are parallel using the transversal angle relationships?
3. What are supplementary angles, and how are they involved in parallel line theory?
4. How can the angle sum property be used to explore transversals?
5. How can we apply parallel line properties in geometric proofs?

**Tip:** When working with transversals, always check for angle congruency or supplementarity, as these are key to proving parallel lines.

Which lines are parallel if ∠3 and ∠5 are congruent?

In this geometry problem, learn how to determine which lines are parallel based on corresponding angles ∠3 and ∠5. Using the corresponding angles postulate, explore how transversals create parallel lines. Ideal for students in grades 8-10.

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