Final answer:
In geometry, parallel lines have identical slopes and never intersect, while perpendicular lines intersect at a 90° angle. These properties are applicable on a coordinate system and in vector operations using geometric methods such as the parallelogram rule.
Step-by-step explanation:
The subject of your geometry question involves understanding the properties of parallel lines and how they interact with perpendicular lines and vectors. Parallel lines have the same slope when plotted on a coordinate system, which means they never intersect and are always equidistant from each other. Perpendicular lines intersect at a 90° angle, forming four right angles at the point of intersection. An example of this is seen on a line graph with x on the horizontal axis and y on the vertical axis, where the y-intercept is the point where the line crosses the y-axis, and the slope of the line determines its angle relative to the x-axis.
In vector operations, such as adding or subtracting vectors using geometric methods, the properties of parallelism and perpendicularity are also useful. For instance, when two vectors are added using the parallelogram rule, and the resultant vector is drawn from the origin to the opposite corner of the parallelogram, the vectors being added are represented by the sides of the parallelogram, which will be parallel to the opposite side, illustrating the concept of parallel lines.