How to draw a perfect triangle. Draw a triangle in Photoshop

How to draw a triangle?

Construction of various triangles is a mandatory element of a school geometry course. For many, this task causes fear. But in fact, everything is quite simple. The following article describes how to draw any type of triangle using a compass and ruler.

There are triangles

versatile;
isosceles;
equilateral;
rectangular;
obtuse-angled;
acute-angled;
inscribed in a circle;
described around a circle.

Construction of an equilateral triangle

An equilateral triangle is one in which all sides are equal. Of all the types of triangles, equilateral triangles are the easiest to draw.

Using a ruler, draw one of the sides at a given length.
Measure its length using a compass.
Place the point of the compass at one end of the segment and draw a circle.
Move the point to the other end of the segment and draw a circle.
We got 2 points of intersection of the circles. By connecting any of them to the edges of the segment, we get an equilateral triangle.

Construction of an isosceles triangle

This type of triangles can be constructed using the base and sides.

An isosceles triangle is one in which two sides are equal. In order to draw an isosceles triangle using these parameters, you must perform the following steps:

Using a ruler, mark off a segment equal in length to the base. We denote it with the letters AC.
Using a compass, measure the required side length.
From point A, and then from point C, we draw circles whose radius is equal to the length of the side.
We get two intersection points. By connecting one of them with points A and C, we obtain the required triangle.

Constructing a right triangle

A triangle with one right angle is called a right triangle. If we are given a leg and a hypotenuse, drawing a right triangle is not difficult. It can be constructed using a leg and a hypotenuse.

Constructing an obtuse triangle using an angle and two adjacent sides

If one of the angles of a triangle is obtuse (more than 90 degrees), it is called obtuse. To draw an obtuse triangle using the specified parameters, you must do the following:

Using a ruler, mark off a segment equal in length to one of the sides of the triangle. Let's denote it by the letters A and D.
If an angle has already been drawn in the assignment, and you need to draw the same one, then on its image put two segments, both ends of which lie at the vertex of the angle, and the length is equal to the indicated sides. Connect the resulting dots. We have the desired triangle.
To transfer it to your drawing, you need to measure the length of the third side.

Construction of an acute triangle

An acute triangle (all angles less than 90 degrees) is constructed using the same principle.

Draw two circles. The center of one of them lies at point D, and the radius is equal to the length of the third side, and the center of the second is at point A, and the radius is equal to the length of the side indicated in the task.
Connect one of the intersection points of the circle with points A and D. The required triangle is constructed.

Inscribed triangle

In order to draw a triangle in a circle, you need to remember the theorem, which states that the center of the circumscribed circle lies at the intersection of the perpendicular bisectors:

For an obtuse triangle, the center of the circumscribed circle lies outside the triangle, while for a right triangle it lies at the middle of the hypotenuse.

Draw a circumscribed triangle

A circumscribed triangle is a triangle in the center of which a circle is drawn touching all its sides. The center of the incircle lies at the intersection of the bisectors. To build them you need:

Construction of a regular hexagon inscribed in a circle. The construction of a hexagon is based on the fact that its side is equal to the radius of the circumscribed circle. Therefore, to construct it, it is enough to divide the circle into six equal parts and connect the found points to each other (Fig. 60, a).

A regular hexagon can be built using a straight edge and a 30X60° square. To carry out this construction, we take the horizontal diameter of the circle as the bisector of angles 1 and 4 (Fig. 60, b), construct sides 1 -6, 4-3, 4-5 and 7-2, after which we draw sides 5-6 and 3- 2.

Constructing an equilateral triangle inscribed in a circle. The vertices of such a triangle can be constructed using a compass and a square with angles of 30 and 60° or just one compass.

Let's consider two ways to construct an equilateral triangle inscribed in a circle.

First way(Fig. 61,a) is based on the fact that all three angles of the triangle 7, 2, 3 contain 60°, and the vertical line drawn through point 7 is both the height and the bisector of angle 1. Since the angle is 0-1- 2 is equal to 30°, then to find the side

1-2, it is enough to construct an angle of 30° from point 1 and side 0-1. To do this, install the crossbar and square as shown in the figure, draw line 1-2, which will be one of the sides of the desired triangle. To construct side 2-3, set the crossbar in the position shown by the dashed lines, and draw a straight line through point 2, which will determine the third vertex of the triangle.

Second way is based on the fact that if you build a regular hexagon inscribed in a circle and then connect its vertices through one, you will get an equilateral triangle.

To construct a triangle (Fig. 61, b), mark the vertex-point 1 on the diameter and draw a diametrical line 1-4. Next, from point 4 with a radius equal to D/2, we describe an arc until it intersects with the circle at points 3 and 2. The resulting points will be the other two vertices of the desired triangle.

Constructing a square inscribed in a circle. This construction can be done using a square and a compass.

The first method is based on the fact that the diagonals of the square intersect in the center of the circumscribed circle and are inclined to its axes at an angle of 45°. Based on this, we install the crossbar and square with angles of 45° as shown in Fig. 62, a, and mark points 1 and 3. Next, through these points we draw the horizontal sides of the square 4-1 and 3-2 using a crossbar. Then, using a straight edge, we draw the vertical sides of the square 1-2 and 4-3 along the leg of the square.

The second method is based on the fact that the vertices of the square bisect the arcs of the circle enclosed between the ends of the diameter (Fig. 62, b). We mark points A, B and C at the ends of two mutually perpendicular diameters and from them with a radius y we describe arcs until they intersect each other.

Next, through the intersection points of the arcs we draw auxiliary straight lines, marked in the figure with solid lines. The points of their intersection with the circle will determine vertices 1 and 3; 4 and 2. We connect the vertices of the desired square obtained in this way in series with each other.

Construction of a regular pentagon inscribed in a circle.

To fit a regular pentagon into a circle (Fig. 63), we make the following constructions.

We mark point 1 on the circle and take it as one of the vertices of the pentagon. We divide the segment AO in half. To do this, we describe an arc from point A with the radius AO until it intersects with the circle at points M and B. By connecting these points with a straight line, we get point K, which we then connect to point 1. With a radius equal to the segment A7, we describe an arc from point K until it intersects with the diametrical line AO at point H. By connecting point 1 with point H, we get the side of the pentagon. Then, using a compass solution equal to the segment 1H, describing an arc from vertex 1 to the intersection with the circle, we find vertices 2 and 5. Having made notches from vertices 2 and 5 with the same compass solution, we obtain the remaining vertices 3 and 4. We connect the found points sequentially with each other.

Constructing a regular pentagon along a given side.

To construct a regular pentagon along a given side (Fig. 64), we divide the segment AB into six equal parts. From points A and B with radius AB we describe arcs, the intersection of which will give point K. Through this point and division 3 on line AB we draw a vertical line.

We get point 1-vertex of the pentagon. Then, with a radius equal to AB, from point 1 we describe an arc until it intersects with the arcs previously drawn from points A and B. The intersection points of the arcs determine the pentagon vertices 2 and 5. We connect the found vertices in series with each other.

Construction of a regular heptagon inscribed in a circle.

Let a circle of diameter D be given; you need to fit a regular heptagon into it (Fig. 65). Divide the vertical diameter of the circle into seven equal parts. From point 7 with a radius equal to the diameter of circle D, we describe an arc until it intersects with the continuation of the horizontal diameter at point F. We call point F the pole of the polygon. Taking point VII as one of the vertices of the heptagon, we draw rays from the pole F through even divisions of the vertical diameter, the intersection of which with the circle will determine the vertices VI, V and IV of the heptagon. To obtain vertices / - // - /// from points IV, V and VI, draw horizontal lines until they intersect with the circle. We connect the found vertices sequentially to each other. A heptagon can be constructed by drawing rays from the F pole and through odd divisions of the vertical diameter.

The above method is suitable for constructing regular polygons with any number of sides.

The division of a circle into any number of equal parts can also be done using the data in Table. 2, which provides coefficients that make it possible to determine the dimensions of the sides of regular inscribed polygons.

Today we will tell you how easy it is to be known as an artist among your friends or to show a girl how versatile you are (oh, they love it!). So let's begin!

We will need: 50 grams for courage, 2 pencils (one hard, the other soft), a sheet of paper, a ruler and an eraser. Let the magic begin!

Step 1.

We draw an ordinary triangle - it should not represent the crown of geometric thought: just connect three lines.

Step 2.

Now draw lines inside, just like ours. Try to make them the same width, you’re not a handyman like us!

Step 3.

Did you draw it? Well done! Now draw again as we showed. We know you're tired, but it'll all be over soon.

Step 4.

We cut off the vertices of the triangle as in the picture.

Step 5.

Now trace all the lines that we have highlighted with a thick pencil, pen or gel pen. Or a marker. Or a felt-tip pen. Maybe I need to make a sandwich?

Step 6.

Erase everything unnecessary. We're close to the goal, see?

Step 7

Then we turned to the gods of Olympus and they drew shadows for us. You draw it yourself.

Step 8

Now you can cut out our creation with a blade or scissors and break the fragile minds of your friends. This triangle is one of the figures that geometrically do not have the right to exist or, in other words, “non-existent figures”.

We hope you liked it, because we tried and stole this lesson on drawing a non-existent triangle step by step. And now you better draw heroes

When I was a “teapot”, I was faced with the need to draw a triangle in Photoshop. Then I was unable to cope with this task without outside help.

It turned out that everything is not as complicated as it might seem at first glance. In this lesson I will share with you my experience in drawing triangles.

There are two (known to me) ways.

The first method allows you to draw an equilateral triangle. To do this we need a tool called "Polygon". It is located in the shapes section on the right toolbar.

This tool allows you to draw regular polygons with a specified number of sides. In our case there will be three of them (sides).

After setting the fill color

Place the cursor on the canvas, hold down the left mouse button and draw our figure. During the creation process, the triangle can be rotated without releasing the mouse button.

Result:

In addition, you can draw a shape without a fill, but with an outline. Contour lines are configured in the top toolbar. Filling, or rather the lack thereof, can also be adjusted there.

I got the following triangles:

You can experiment with the settings to achieve the desired result.

The next tool for drawing triangles is "Straight-line lasso".

This tool allows you to draw triangles with any proportions. Let's try to draw a rectangular one.

For a right triangle, we will need to accurately draw a right (who would have thought...) angle.

Let's use the guides. How to work with guide lines in Photoshop, read this article.

So, we read the article, let’s pull the guides. One vertical, the other horizontal.

To make the selection “attracted” to the guides, turn on the snap function.

Then right-click inside the selection and select, depending on your needs, context menu items "Perform Fill" or "Stroke".

The fill color is configured as follows:

The stroke width and position can also be adjusted.

We get the following results:
Filling.

To obtain sharp corners, the stroke must be done "Inside".

After deselecting ( CTRL+D) we get a finished right triangle.

These are the two simplest ways to draw triangles in Photoshop.

In this article, you will learn how to draw different types of triangles in Photoshop: equilateral, isosceles, scalene and rectangular.

How to draw an equilateral triangle

An equilateral triangle has all three sides equal.

The easiest way to draw such a triangle in Photoshop is to use Polygon tool.

Select this tool and in the settings panel immediately specify the number of sides - 3.

The next step is to decide what the future triangle should be: a vector shape, a raster shape with a solid fill, or just an outline is needed. Consider all options.

Vector triangle

In the options bar, select the option Shape layer.

Now you can draw the triangle itself. During creation, you will see its boundaries. This is necessary in order to calculate its dimensions. Also, until you release the mouse button, you can rotate it.

The good thing about a vector triangle is that you can quickly change its color, as well as painlessly change its size without losing quality. To do this, call the command - Ctrl+T.

To later turn it into a raster triangle, use the command.

Raster triangle with solid fill

You will get the same triangle as in the example above, but it will be immediately in the raster.

To do this, in the options bar you need to select the setting Fill pixels.

Before creating such a triangle, you must first.

Now draw a shape and it will be like the most ordinary bitmap element.

How to Draw the Outline of an Equilateral Triangle

For such a shape, select the option in the options bar Outlines.

Draw a triangle. Naturally, you will only get its outline. Next, with the same tool selected, right-click inside the path. A context menu will appear. Select a team Create a selection area.

A dialog box will open. Leave the feathering radius at 0. Click OK.

As a result, we made it from the outline.

To do this, run the command Editing - Stroke. A window will appear in which you specify the thickness of the stroke line, as well as how it will pass relative to the dotted selection line: inside, in the center, outside.

Photoshop has made a stroke, now remove the dotted selection line so that it does not interfere - Ctrl+D. Result:

How to draw an isosceles triangle

An isosceles triangle has two equal sides.

Let's look at an example when you need to draw an isosceles triangle of given dimensions. Let's say the base is 300 pixels and the height is 400 pixels.

Ready

An isosceles triangle is drawn according to the given dimensions!

In a right triangle, one of the angles is 90 degrees.

If you need a right triangle with pre-known dimensions, for example, the dimensions of the legs are 200 and 300 pixels, then the easiest way to do this is as follows:

Step 1

Create a new document in Photoshop with the height and width equal to the dimensions of the legs: for example, let the width be 300 pixels and the height 200 pixels.

The work area in Photoshop is always rectangular, so an angle of 90 degrees will already be provided. The two sides of a rectangle are its legs. All that remains is to draw the diagonal - this will be the hypotenuse.

Step 2

We will proceed by analogy with the example above. Take the tool Line and set the option Shape layer.

Now draw a line around the edges and connect two points diagonally: