What is the vertical line symbol

Perpendicular and perpendicular to

Straight lines or stretches can be in special positions to each other. This is about "vertical".

But "vertical" means something different in colloquial language than in mathematical language.

Example:
Aylin and Tina want to break a vertical stick on a mountain. It is easier for young trees to grow straight up on such a stick.

You do this:



Who thought correctly?
For the answer, imagine how trees grow in nature. They grow the way Aylin dug the stick into the ground.

In colloquial language, you describe Aylin's staff as vertical.

Mathematically speaking, Tina's staff is perpendicular to the mountain. Mathematically, “perpendicular to something” means that the angle between the two imaginary lines (here rod and mountain) is 90 °.



Aylin's staff is vertical as you feel it. Your body automatically applies this notion of vertical when you climb a mountain. Buildings are also built vertically.



Mathematically vertical - pretty useless at first glance? :-)

In colloquial language, the opposite of “vertical” is the word “horizontal”. The water surface of a lake is horizontal.

A right angle is 90 °. This is the symbol for a right angle:

You also say that you the plumb bob falls on somethingwhen you talk about vertical.



Here, the weighted tape is used to check whether the wall is vertical. The tape is the plumb line here.

"Perpendicular to" with two straight lines

How do you draw two vertical lines?

Take your set square. Put the Center line of the set square on the straight line. Draw a straight line along the measuring stick.



Then you have a straight line perpendicular to the starting line.



You can also draw the right angle. There are four of them at the straight intersection. But it is enough if you draw one.

Two lines or lines are perpendicular to each other if the angle between them is 90 °.
The technical term for "perpendicular to" is "orthogonal to". You can use both words equally.

Vertical straight line through a point

Often you don't have to draw just any perpendicular line to another, but rather a perpendicular line through one certain point. The perpendicular line to the other is then called “perpendicular”.



Place the set square with the center line on the straight line. Slide the set square until you reach the point. It doesn't matter which direction you're pushing from.



If your set square is correct, you will draw the perpendicular.



Most of the time the lines are called $$ g $$ and $$ h $$.



There is a symbol for two vertical straight lines. It looks like this: $$ bot $$

If two straight lines $$ g $$ and $$ h $$ are perpendicular to each other, you write $$ g bot h $$.

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Verticals in everyday life

You encounter vertical stretches very often:

Urban planning

For cities, it is convenient if streets and cross streets are perpendicular to each other. Most buildings have right angles because the walls are perpendicular to each other. Streets that run perpendicular to each other offer the best possible use of space. Some cities are therefore specially planned. (Whether that is also nice is a matter of taste. :-) But it is practical.)

This is very perfectly applied in parts of New York. Here you can see the island of Manhattan with its streets.



Image: Joachim Zwick

Building construction

In red you can see lines that are perpendicular to the floor surface.


This is the town hall in Greifswald.

Or on a small scale

Fold paper

For example, if you want to fold a star, you start by creasing the paper in the middle. The resulting kink lines are perpendicular to each other.

Letters

The writing you read is based in part on vertical lines. Typical letters with mutually perpendicular lines are H or L..

Furniture making

In furniture construction, you need right angles for cupboards, for example. The wall units should be perpendicular to each other. To do this, you have to be able to draw vertical lines on a board. Or you check whether the boards are really perpendicular to each other.

Professionals use this tool instead of a set square. That is a Stop bracket.


Perpendiculars in mathematics

In mathematics, you need lines that are perpendicular to each other in a square or rectangle.



In the case of solids, there are vertically aligned edges in the cube and cuboid.



If you draw a height of a figure, this is also perpendicular to the baseline.



The height $$ h $$ is perpendicular to the segment.

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Construct vertical lines with the compass

You can also construct a vertical line with the compass if you don't have a set square. (Math freaks prefer to use the circle than the set square. :-))

Then proceed as follows:

1. Stitch the straight line with the compass. Set any compass span.




2. Use the compass span to make two marks on the straight line. These are equidistant from the puncture site.




3. Stitch in the first marking and make the compass span a little wider.
(Don't make it too wide, otherwise the drawing will be so big. You can also leave the radius set up to the point.)
Draw an arc around the first marking in the direction of the vertical.




4. Do not change the setting and draw a second arc from the other marking.




5. You get two points of intersection on the arcs. You connect these. The vertical is finished.


This vertical bisects the distance between the 2 marking points on the straight line.

Perpendicular to a straight line through a point

This is what it looks like if there is still a point P.



This is how you do it:

1. Stitch in point P. Draw an arc of a circle that intersects the line twice. There are 2 marks on the straight line.




2. Stitch into one of the markings with the same or greater circle span. Draw an arc in the direction of the vertical.




3. Do not change the setting and draw a second arc from the other marking.




4. Connect the 2 intersection points of the arcs with a straight line. Your vertical is ready.