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Identify perpendicular lines

Perpendicular lines are lines that intersect to form four right angles, so their directions meet at 90 degrees; they may be horizontal, vertical, or differently oriented and need not be the same length. The relationship can be identified in geometric drawings and real-world figures, distinguishing perpendicular lines from merely crossing or parallel lines, and supports understanding of right angles, rectangles, squares, and later geometric measurement; formal equations, slopes, and more advanced angle relationships are not included.

Detailed Explanation: Identify perpendicular lines

Perpendicular lines are lines that meet to make a right angle. A right angle measures 90∘90^\circ. The lines do not have to be the same length, and they can be horizontal, vertical, or slanted.

To identify perpendicular lines:

  1. Find where the lines meet.
  2. Look at the angle they form.
  3. If the angle is a square corner, the lines are perpendicular.
  4. If they do not meet, they are not perpendicular. If they meet but do not make a right angle, they are simply crossing lines.

Example

Look at rectangle ABCDABCD:

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

Which sides are perpendicular to side AB‾\overline{AB}?

  • AB‾\overline{AB} meets BC‾\overline{BC} at point BB.
  • The corner at BB is a right angle, so AB‾⊥BC‾\overline{AB} \perp \overline{BC}.
  • AB‾\overline{AB} also meets AD‾\overline{AD} at point AA.
  • The corner at AA is a right angle, so AB‾⊥AD‾\overline{AB} \perp \overline{AD}.

Therefore, the sides perpendicular to AB‾\overline{AB} are BC‾ and AD‾\boxed{\overline{BC}\text{ and }\overline{AD}}. The side CD‾\overline{CD} is parallel to AB‾\overline{AB} because they do not meet.

Learn by doing: Identify perpendicular lines

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