Question

How are parallel and perpendicular lines alike?

Answer 1

Hint: Straight lines are the most basic part of geometry. When these straight lines are drawn together, they form certain patterns and figures. There are two types of basic lines, namely parallel and perpendicular lines. We shall discuss their properties in order to comment upon how they are alike.

Complete step-by-step solution:
Parallel lines are the group of lines in the same plane which never intersect with each other. In the diagrams or figures provided in various geometrical problems, we might just look at the set of lines and comment whether they are parallel or not. However, this prediction can be incorrect sometimes. One proper way of identifying parallel lines is that the line intersecting these lines will make equal angles with every line if the lines it is intersecting are parallel.

If line PQ is parallel to line RS and line UV intersects them, then
$\Rightarrow \angle A=\angle B$
Angles A and B are called corresponding angles.
Perpendicular lines are the lines that bisect each other at an angle of ${{90}^{\circ }}$. Perpendicular lines are represented by making a small half-square as the angle between them in the commonly drawn mathematical figures and diagrams.
In this diagram line AB is perpendicular to line CD is represented by the small box made in place of the angle between the two lines.

Therefore, we observe that parallel and perpendicular lines are completely different and the only thing alike between them is that both of them consist of straight lines.

Note: The parallel lines are represented by writing two bars, $\parallel $ symbol in the geometrical notation whereas the geometrical notation of perpendicular lines is given as $\bot $ symbol. We must be well aware of the basic geometrical symbols in order to understand and further solve the geometrical problems.