Perpendicular and parallel lines
Distinguish perpendicular and parallel lines and check corresponding- and alternate-angle conditions.
Meaning
Two coplanar lines that never meet are parallel; lines meeting at a right angle are perpendicular. A transversal through parallel lines makes equal corresponding and equal alternate angles. Translate one intersection to the other along the transversal. The transversal maps to itself and one parallel line maps to the other. Translation preserves angles, giving equal corresponding angles; vertical angles then connect the alternate angles.
Example
If one corresponding angle formed by a transversal through parallel lines is 65 degrees, its partner is also 65 degrees. Being corresponding or alternate describes position, not automatic equality. Equality needs the parallel-line condition.
Practice for this concept
Scope and references
Topics
Perpendicular lines, perpendiculars, parallel lines, corresponding and alternate angles
Learning goal
Distinguish perpendicular and parallel lines and check corresponding- and alternate-angle conditions.
Helpful background
Check angles and the relative positions of lines.
Perpendicular and parallel lines
These choice exercises use stated geometric conditions. They do not establish construction, drawing, spatial manipulation, written proof, or mastery of the whole geometry area.