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In this diagram, lines \( g \) and \( f \) are parallel, and a transversal crosses them, forming eight angles. The task asks for three angles congruent to \( \angle 1 \) and justifies the reasoning behind each choice. 

Let's break this down:

1. **\( \angle 3 \) is congruent to \( \angle 1 \)** because they are **vertically opposite angles**. When two lines intersect, opposite angles are always congruent.

2. **\( \angle 5 \) is congruent to \( \angle 1 \)** because they are **corresponding angles**. When a transversal crosses two parallel lines, corresponding angles are congruent. Angle \( 1 \) corresponds to angle \( 5 \) since they are on the same side of the transversal and in matching positions relative to lines \( g \) and \( f \).

3. **\( \angle 7 \) is congruent to \( \angle 1 \)** because they are **alternate interior angles**. For two parallel lines crossed by a transversal, alternate interior angles are congruent. Angles \( 1 \) and \( 7 \) lie on opposite sides of the transversal and inside the parallel lines.

Would you like further details or explanations on any part of this reasoning?

Here are 5 relative questions for further exploration:
1. What other angle relationships exist between transversal and parallel lines?
2. How can you determine when angles are supplementary versus congruent?
3. What is the difference between alternate interior and alternate exterior angles?
4. How does this concept extend to non-parallel lines crossed by a transversal?
5. Can we apply similar angle relationships in 3D geometry?

**Tip:** Always check if lines are parallel when analyzing angle relationships with a transversal, as many angle properties rely on this condition.

In the figure below, lines g and f are parallel. Name 3 angles that are congruent to ∠1 (angle #1) and justify your reasoning.

Identify and justify three angles congruent to ∠1 in a diagram with parallel lines and a transversal. This problem covers key concepts like corresponding angles, alternate interior angles, and vertical angles. Suitable for students in Grades 8-10.

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