Parallel Lines
Lines in the same plane that neverintersect
Parallel lines are two or more lines that never intersect or meet, regardless of how far they are extended. They are always at the same distance from each other and have the same slope. In other words, two lines are parallel if they have the same slope and do not intersect.
Parallel lines have some important properties:
– They have equal slopes: If two lines are parallel, then their slopes are equal. The slope of a line is the ratio of change in y-coordinate to change in x-coordinate, and can be expressed as a fraction or decimal.
– They never meet: Two parallel lines never intersect or meet, no matter how far they are extended in either direction.
– They have similar angles: When a transversal (a line intersecting two parallel lines) is drawn, the corresponding angles, alternate angles, and interior angles are equal.
– They have the same perpendicular distance: The distance between two parallel lines is the same at any point along their length. This distance is measured perpendicular to the lines.
Parallel lines can be represented mathematically using the slope-intercept form of a line: y = mx + b. Two lines are parallel if they have the same slope (m) and different y-intercepts (b). For example, the lines y = 2x + 3 and y = 2x + 7 are parallel because they have the same slope of 2 but different y-intercepts of 3 and 7, respectively.
Parallel lines are commonly found in geometry, trigonometry, and algebra. They have many applications in real life, such as in the design and construction of buildings, roads, and bridges.
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