In the figure to the​ right, s double vertical line ts∥t. Use the figure to answer the following exercise.

Question

angle f∠f is congruent to which two of the following​ angles?
aab Superscript b Subscript Baseline c cddeeSubscript Baseline f f
s
t
u


Lines s and t are parallel, horizontal lines. Line s is above line t. Line u is a transversal that falls from left to right, intersecting lines s and t, forming 4 angles at each intersection. From left to right above and below each horizontal line, the angles are labeled as follows: above line s, f and e; below line s, a and b; above line t, c and d; below line t, unlabeled and unlabeled.
Question content area bottom
Part 1
Select all that apply.
angle e
angle e∠e
angle a
angle a∠a
angle b
angle b∠b
angle c
angle c∠c
Select all that apply.

Answer 1

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:

1. 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.

2. 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.

3. 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 \( f \):

• 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 \( e \).

• 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