Two parallel lines are intersected by a third line so that angles 1 and 5 are congruent.

2 parallel horizontal lines are intersected by a third line. On the first horizontal line where the third line intersects, 4 angles are created. Labeled clockwise, from uppercase left, the angles are 1, 2, 4, 3. On the second horizontal line, where the third line intersects, 4 angles are created. Labeled clockwise, from uppercase left, the angles are 5, 6, blank, blank.
Which statement is true about angles 3 and 5?

They are acute.
They are congruent.
They are complementary.
They are supplementary.

In this problem, two parallel lines are intersected by a third line, forming two sets of angles. The key information is that angles 1 and 5 are congruent. Let’s break down the relationships between the angles:

1. **Angles 1 and 5 are congruent** because they are corresponding angles formed by the transversal intersecting two parallel lines.

2. **Angles 1 and 3** are vertical angles (since they are opposite each other at the intersection point on the first line), and **vertical angles are congruent**.

3. Therefore, since angles 1 and 3 are congruent, and angle 1 is congruent to angle 5, **angles 3 and 5 must also be congruent**.

### Answer: **They are congruent**.

Would you like more details on angle relationships or parallel line theorems? 

Here are 5 follow-up questions to explore further:

1. What are alternate interior angles, and how do they relate to this problem?
2. How can you prove that angles 3 and 5 are congruent using a geometric theorem?
3. What are the properties of supplementary angles in this setup?
4. How do complementary and supplementary angles differ?
5. Can you explain how vertical angles are formed?

**Tip**: When two parallel lines are intersected by a transversal, corresponding angles are always congruent.

Two parallel lines are intersected by a third line so that angles 1 and 5 are congruent. Which statement is true about angles 3 and 5?
They are acute.
They are congruent.
They are complementary.
They are supplementary.

Explore how two parallel lines intersected by a transversal form congruent angles. This problem focuses on key geometry concepts like corresponding angles, vertical angles, and the relationship between angles 3 and 5. Suitable for students in Grades 8-10.

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