In the given scenario, you have two parallel lines \( s \) and \( t \) with a transversal \( u \) intersecting them. When two parallel lines are intersected by a transversal, certain angle relationships hold due to the properties of parallel lines.
Let's break down the angles:
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Corresponding Angles: Angles that are in the same position at each intersection. For example, if angle \( f \) is above line \( s \) and angle \( c \) is above line \( t \) and in the same position, they are congruent.
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Alternate Interior Angles: Angles that are on opposite sides of the transversal and inside the two parallel lines. For example, angle \( e \) (above line \( s \)) and angle \( b \) (below line \( t \)) are alternate interior angles, making them congruent.
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Alternate Exterior Angles: Angles that are on opposite sides of the transversal but outside the two parallel lines.
Using these rules, we can identify which angles are congruent to angle \( f \):
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Angle \( e \) is an alternate interior angle to angle \( f \) (on the same side of the transversal and below line \( s\)). Therefore, angle \( f \) is congruent to angle \( e \).
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Angle \( b \) is also an alternate interior angle that pair with \( f \) (on the same side of the transversal and on the same vertical line as \( f\)). Hence, angle \( f \) is congruent to angle \( b \).
Thus, the angles that are congruent to angle \( f \) are:
- Angle \( e \)
- Angle \( b \)
So, the correct selections would be:
- angle e
- angle b