Question

How are perpendicular lines similar to intersecting lines? How are they different?

Answer 1

Hint: To solve these types of questions, first we need to have a clear understanding of what perpendicular and intersecting lines are. Perpendicular lines make an angle of \[{90^ \circ }\] between them. Intersecting lines are lines which meet each other at any point.

Complete step by step solution:
Firstly , we know that intersecting lines are simply two lines which intersect each other at some point, that is they meet each other at some point. While perpendicular lines are the lines which intersect each other at \[{90^ \circ }\], that is they form an angle of \[{90^ \circ }\] between them.
The similarity between the intersecting line and perpendicular lines is that in both the cases the given lines need to intersect at some point, that means for two lines to be intersecting or for two lines to be perpendicular a common necessary condition is that both the lines have to meet.
Now perpendicular lines are intersecting lines that intersect at a specific angle that is \[{90^ \circ }\]. However in general intersecting lines can be any two lines that meet each other making any angle between them. Thus the difference between perpendicular and intersecting lines is that perpendicular lines need to intersect at a specific angle that is \[{90^ \circ }\], while intersecting lines in general can make any angle between them.

Note: Remember that all perpendicular lines are intersecting lines but all intersecting lines are not perpendicular lines. This means that if two lines are perpendicular then they have to be intersecting, but if two lines are intersecting, it is not necessary that they will always be perpendicular. Thus, note that perpendicular lines are a special form of intersecting lines.