Final answer:
The subject question deals with Geometry in Mathematics, specifically regarding lines that are parallel or perpendicular to one another. Parallel lines never intersect, while perpendicular lines do at a 90-degree angle. Different contexts within the question show how these concepts apply to shapes, vectors, and graphs.
Step-by-step explanation:
The question provided seems to involve the concepts of parallel and perpendicular lines, which are fundamental elements of Geometry, a branch of Mathematics. When two lines are parallel to each other, they never intersect no matter how far they are extended on both ends. For lines to be perpendicular, they must intersect at a right angle (90 degrees). Understanding these concepts can help us approach problems involving the properties and relations of lines in a plane.
For example, when we say line A'C is parallel to line AC, this means both lines extend in the same direction without ever meeting. Similarly, if line PQ is stated to be parallel to line PQ, it implies that it is indeed the same line (as a line is always parallel to itself). Perpendicularity introduces a different relationship, referring to lines that intersect at right angles. In Geometrical notation, line AC being perpendicular to line AC is an impossibility unless we are discussing distinct lines with the same naming convention, in which case a context needs to be provided.
The given examples illustrate scenarios where lines are either parallel or perpendicular to one another in various contexts, including geometrical shapes like triangles, vector operations in Physics, and the analysis of increasing or decreasing lines in graphical representations.