Questions: 9. angle 2 congruent to angle 9 10. angle 6 congruent to angle 7 11. angle 2 congruent to angle 5 12. angle 5 congruent to angle 9 13. angle 3 congruent to angle 11 14. angle 8 + angle 5 + angle 6 congruent to 180 15. line FC perpendicular to line AE line FC perpendicular to line BD

Solution Steps

To determine which segments must be parallel based on the given angle congruences, we can use the properties of parallel lines and transversals. Specifically, if corresponding angles or alternate interior angles are congruent, then the lines are parallel.

1. $\angle 2 \cong \angle 9$: If these angles are corresponding angles or alternate interior angles, then the lines they are associated with are parallel.
2. $\angle 6 \cong \angle 7$: If these angles are corresponding angles or alternate interior angles, then the lines they are associated with are parallel.
3. $\angle 2 \cong \angle 5$: If these angles are corresponding angles or alternate interior angles, then the lines they are associated with are parallel.

Given the angle congruences:

1. \( \angle 2 \cong \angle 9 \)
2. \( \angle 6 \cong \angle 7 \)
3. \( \angle 2 \cong \angle 5 \)

We will analyze these relationships to determine which lines must be parallel.

Using the properties of parallel lines:

• If \( \angle 2 \cong \angle 9 \), then the lines associated with these angles are parallel.
• If \( \angle 6 \cong \angle 7 \), then the lines associated with these angles are parallel.
• If \( \angle 2 \cong \angle 5 \), then the lines associated with these angles are parallel.

From the angle relationships, we conclude:

• Lines associated with \( \angle 2 \) and \( \angle 9 \) are parallel.
• Lines associated with \( \angle 6 \) and \( \angle 7 \) are parallel.
• Lines associated with \( \angle 2 \) and \( \angle 5 \) are parallel.

Final Answer