## parallel lines

### Parallel lines are two lines in a plane that never intersect or cross each other

Parallel lines are two lines in a plane that never intersect or cross each other. In other words, they maintain a constant distance between each other at all points. This constant distance between parallel lines is referred to as the “gap” or “distance” between them.

Visually, parallel lines appear as straight lines running alongside each other, maintaining a consistent and identical distance apart. No matter how far the lines extend, they will never intersect, no matter how far they are extended.

Symbolically, parallel lines are denoted by the symbol “||.” For example, if line AB is parallel to line CD, it is written as AB || CD. The symbol emphasizes the fact that the lines do not intersect and run alongside each other.

It is also worth noting that parallel lines can be present in various geometric shapes, including rectangles, squares, and triangles. Additionally, parallel lines have several important properties:

1. Transversal: When a third line (called a transversal) intersects two parallel lines, it forms pairs of corresponding angles, alternate interior angles, and alternate exterior angles that have specific relationships.

2. Angle relationships: Corresponding angles are congruent, meaning they have the same measure. Alternate interior angles and alternate exterior angles are also congruent.

3. Slopes: If two lines in a coordinate plane have the same slope, they are parallel. The slope-intercept form of a line (y = mx + b) can help determine if two lines are parallel by comparing their slopes (m-values). If the slopes are equal, the lines are parallel.

Understanding parallel lines and their properties is crucial in geometry and can help solve various problems, such as finding missing angles or identifying congruent shapes.

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