Ctrl+k

Identify perpendicular lines

Perpendicular lines are two lines that intersect to form four right angles; their orientation on the page does not matter, so both vertical-and-horizontal and slanted pairs may be perpendicular. The learner identifies perpendicular pairs in drawings and familiar plane figures by relating their intersection to a square corner, distinguishing them from parallel lines or lines that merely meet; slope calculations and formal angle measurement are not included.

Detailed Explanation: Identify perpendicular lines

Perpendicular lines are lines that cross to make four square corners, called right angles. The lines can be vertical, horizontal, or slanted. Their direction on the page does not matter.

To check whether two lines are perpendicular:

  1. Find where the lines cross.
  2. Look at the corners made by the crossing.
  3. Ask: “Do the corners look like the corner of a square?”
  4. If all four corners are square corners, the lines are perpendicular.

Example:

Look at rectangle (ABCD)(ABCD):

A -------- B
|          |
|          |
D -------- C

Are AB‾\overline{AB} and BC‾\overline{BC} perpendicular?

  • The lines AB‾\overline{AB} and BC‾\overline{BC} meet at point BB.
  • At BB, they form a square corner.
  • The other corners made by these two lines are also right angles.
  • Therefore, AB‾\overline{AB} and BC‾\overline{BC} are perpendicular.

We can write:

AB‾⊥BC‾\overline{AB} \perp \overline{BC}

The symbol ⊥\perp means “is perpendicular to.” Lines that never meet are parallel, and lines that meet without making square corners are not perpendicular.

Learn by doing: Identify perpendicular lines

Click a topic below to practice the foundational skills you'll need, learn the steps, or master this skill

    Practice with unlimited practice problems

    Identify Whether Lines are Intersecting, Parallel, or Perpendicular

      ?