The original worked lessons remain the main explanations. Use these focused reminders to check the conditions before you start.
Parallel, perpendicular and exceptional lines
Use equal gradients and negative reciprocals correctly.
Handle horizontal and vertical lines without division by zero.
Distinguish coincident lines from distinct parallel lines; construct perpendicular bisectors.
For nonvertical lines, parallel directions have equal gradients. For two nonvertical perpendicular lines, \(m_1m_2=-1\). A vertical line \(x=a\) is perpendicular to a horizontal line \(y=b\). Equal gradients do not establish that two lines are distinct.