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Identify perpendicular lines

Perpendicular lines intersect to form right angles, each measuring 90°; when two full lines intersect perpendicularly, all four angles at the intersection are right angles. Their orientation may be horizontal, vertical, or slanted, so merely crossing lines are not necessarily perpendicular. Identification relies on the right-angle relationship, not on slopes, equations, or coordinate calculations.

Detailed Explanation: Identify perpendicular lines

Perpendicular lines are lines that meet to make a right angle. A right angle measures 90∘90^\circ.

To identify perpendicular lines:

  1. Find where the two lines intersect.
  2. Look at the angles formed at the intersection.
  3. Check whether the angles are right angles, often shown by a small square.
  4. If the lines are full lines, all four angles at the intersection will measure 90∘90^\circ.

Example

Suppose lines AB↔\overleftrightarrow{AB} and CD↔\overleftrightarrow{CD} intersect. The diagram shows a small square at the intersection, so one angle measures 90∘90^\circ.

Because the two are full lines, the other three angles at the intersection are also right angles:

90∘, 90∘, 90∘, 90∘90^\circ,\ 90^\circ,\ 90^\circ,\ 90^\circ

Therefore, AB↔\overleftrightarrow{AB} and CD↔\overleftrightarrow{CD} are perpendicular lines.

Remember: Lines do not have to be horizontal and vertical to be perpendicular. Slanted lines can also be perpendicular if they meet to form 90∘90^\circ angles. Simply crossing is not enough.

Learn by doing: Identify perpendicular lines

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    Geometry of Lines - Crossing Perpendicular Lines Solve Angle

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