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Identify parallel and perpendicular lines

Parallel lines are coplanar lines that remain the same distance apart and do not intersect, even when extended; perpendicular lines intersect to form four right angles. The understanding applies to lines, line segments, and rays in drawings and coordinate grids, including orientations that are not horizontal or vertical, and supports later reasoning about angle relationships, geometric figures, and coordinate geometry without requiring formal slope calculations.

Detailed Explanation: Identify parallel and perpendicular lines

To identify parallel and perpendicular lines, look at how the lines are positioned:

  • Parallel lines stay the same distance apart and never meet, even if extended.
  • Perpendicular lines meet to form a square corner, or a right angle of 90∘90^\circ.

Example:
A slanted quadrilateral ABCDABCD has these markings:

  • ABAB and CDCD have matching arrow marks.
  • BCBC and ADAD have a different set of matching arrow marks.
  • Angle ABCABC has a small square marking.

Step 1: Find the parallel sides.
Matching arrow marks show that the sides have the same direction.

Therefore,

AB‾∥CD‾\overline{AB} \parallel \overline{CD}

and

BC‾∥AD‾.\overline{BC} \parallel \overline{AD}.

These opposite sides would remain the same distance apart and would not meet if extended.

Step 2: Find the perpendicular sides.
The square marking at angle ABCABC shows that AB‾\overline{AB} and BC‾\overline{BC} meet to form a right angle.

Therefore,

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

So, the answer is:

  • Parallel: AB‾\overline{AB} and CD‾\overline{CD}; BC‾\overline{BC} and AD‾\overline{AD}
  • Perpendicular: AB‾\overline{AB} and BC‾\overline{BC}

Remember: same direction and no meeting means parallel; a square corner means perpendicular.

Learn by doing: Identify parallel and perpendicular lines

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