Parallel Lines 60C9Ba
1. The problem asks to complete the statement: "Parallel lines always have the same ____________." The options are y-intercept, x-intercept, and gradient.
2. In geometry, parallel lines are lines in a plane that never meet; they have the same slope or gradient but different intercepts.
3. Therefore, the correct completion is: Parallel lines always have the same **gradient**.
4. Next, we analyze which lines among A, B, C, and D are parallel based on their slopes.
5. Line A is vertical, so its slope is undefined.
6. Line C has a positive slope.
7. Lines B and D have negative slopes.
8. Since parallel lines must have the same slope, lines B and D are parallel to each other because they both have negative slopes.
9. Line A is vertical and does not share slope with any other line, so it is not parallel to any other line.
10. Line C has a positive slope and is not parallel to lines B or D.
Final answers:
- Parallel lines always have the same **gradient**.
- Lines B and D are parallel to each other.