How to draw a triangle?
The construction of various triangles is a mandatory element of the school geometry course. For many, this task is intimidating. But in fact, everything is quite simple. The rest of the article describes how to draw any type of triangle using a compass and straightedge.
Triangles are
- versatile;
- isosceles;
- equilateral;
- rectangular;
- obtuse;
- acute-angled;
- inscribed in a circle;
- circumscribed around a circle.
Construction of an equilateral triangle
An equilateral triangle is a triangle in which all sides are equal. Of all the types of triangles, drawing an equilateral one is the easiest. 
- Using a ruler, draw one of the sides of a given length.
- Measure its length with a compass.
- Place the point of the compass at one end of the line and draw a circle.
- Move the tip to the other end of the segment and draw a circle.
- We have 2 points of intersection of the circles. Connecting any of them with the edges of the segment, we get an equilateral triangle.
Construction of an isosceles triangle
This type of triangles can be built on the base and sides.
An isosceles triangle is one in which two sides are equal. In order to draw an isosceles triangle according to these parameters, you must perform the following steps: 
- Using a ruler, set aside a segment equal in length to the base. We denote it by the letters AC.
- With a compass we measure the required length of the side.
- We draw from point A, and then from point C, circles whose radius is equal to the length of the side.
- We get two points of intersection. By connecting one of them with points A and C, we get the necessary triangle.
Construction of a right triangle
A triangle with one right angle is called a right triangle. If we are given a leg and a hypotenuse, it will not be difficult to draw a right triangle. It can be built along the leg and hypotenuse.
Construction of an obtuse-angled triangle given an angle and two adjacent sides
If one of the angles of a triangle is obtuse (greater than 90 degrees), it is called an obtuse angle. To draw an obtuse triangle according to the specified parameters, you must do the following: 
- Using a ruler, set aside a segment equal in length to one of the sides of the triangle. Let's call it A and D.
- If an angle has already been drawn in the task, and you need to draw the same one, then on its image set aside two segments, both ends of which lie at the vertex of the angle, and the length is equal to the indicated sides. Connect the dots. We have the required 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 built on 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, while the center of the second is at point A, and the radius is equal to the length of the side specified in the task.
- Connect one of the intersection points of the circle with points A and D. The desired triangle is built.
inscribed triangle
In order to draw a triangle in a circle, you need to remember the theorem, which says 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, and for a right triangle, it lies in the middle of the hypotenuse.
Draw a circumscribed triangle
The described triangle is a triangle in the center of which a circle is drawn, touching all its sides. The center of the inscribed circle lies at the intersection of the bisectors. To build them you need:
Even preschool children know what a triangle looks like. But with what they are, the guys are already starting to understand at school. One type is an obtuse triangle. To understand what it is, the easiest way is to see a picture with its image. And in theory, this is what they call the "simplest polygon" with three sides and vertices, one of which is
Understanding concepts
In geometry, there are such types of figures with three sides: acute-angled, right-angled and obtuse-angled triangles. Moreover, the properties of these simplest polygons are the same for all. So, for all the listed species, such an inequality will be observed. The sum of the lengths of any two sides is necessarily greater than the length of the third side.
But in order to be sure that we are talking about a complete figure, and not about a set of individual vertices, it is necessary to check that the main condition is met: the sum of the angles of an obtuse triangle is 180 o. The same is true for other types of figures with three sides. True, in an obtuse triangle one of the angles will be even more than 90 o, and the remaining two will necessarily be sharp. In this case, it is the largest angle that will be opposite the longest side. True, these are far from all the properties of an obtuse triangle. But even knowing only these features, students can solve many problems in geometry.
For every polygon with three vertices, it is also true that by continuing any of the sides, we get an angle whose size will be equal to the sum of two non-adjacent internal vertices. The perimeter of an obtuse triangle is calculated in the same way as for other shapes. It is equal to the sum of the lengths of all its sides. To determine the mathematicians, various formulas were derived, depending on what data was initially present.
Correct style
One of the most important conditions for solving problems in geometry is the correct drawing. Mathematics teachers often say that it will help not only visualize what is given and what is required of you, but also get 80% closer to the correct answer. That is why it is important to know how to construct an obtuse triangle. If you just want a hypothetical figure, then you can draw any polygon with three sides so that one of the angles is greater than 90 degrees.
If certain values of the lengths of the sides or degrees of angles are given, then it is necessary to draw an obtuse-angled triangle in accordance with them. At the same time, it is necessary to try to depict the angles as accurately as possible, calculating them with the help of a protractor, and display the sides in proportion to the given conditions in the task.
Main lines
Often, it is not enough for schoolchildren to know only how certain figures should look. They cannot limit themselves to information about which triangle is obtuse and which is right-angled. The course of mathematics provides that their knowledge of the main features of the figures should be more complete.
So, each student should understand the definition of the bisector, median, perpendicular bisector and height. In addition, he must know their basic properties.
So, the bisectors divide the angle in half, and the opposite side into segments that are proportional to the adjacent sides.
The median divides any triangle into two equal areas. At the point at which they intersect, each of them is divided into 2 segments in a ratio of 2: 1, when viewed from the top from which it originated. In this case, the largest median is always drawn to its smallest side.
No less attention is paid to height. This is perpendicular to the opposite side from the corner. The height of an obtuse triangle has its own characteristics. If it is drawn from a sharp vertex, then it falls not on the side of this simplest polygon, but on its extension.
The perpendicular bisector is the line segment that comes out of the center of the face of the triangle. At the same time, it is located at a right angle to it.
Working with circles
At the beginning of the study of geometry, it is enough for children to understand how to draw an obtuse-angled triangle, learn to distinguish it from other types and remember its basic properties. But for high school students this knowledge is not enough. For example, at the exam, there are often questions about circumscribed and inscribed circles. The first of them touches all three vertices of the triangle, and the second has one common point with all sides.
Constructing an inscribed or circumscribed obtuse-angled triangle is already much more difficult, because for this you first need to find out where the center of the circle and its radius should be. By the way, in this case, not only a pencil with a ruler, but also a compass will become a necessary tool.
The same difficulties arise when constructing inscribed polygons with three sides. Mathematicians have developed various formulas that allow you to determine their location as accurately as possible.
Inscribed Triangles
As mentioned earlier, if the circle passes through all three vertices, then this is called the circumscribed circle. Its main property is that it is the only one. To find out how the circumscribed circle of an obtuse triangle should be located, it must be remembered that its center is at the intersection of the three median perpendiculars that go to the sides of the figure. If in an acute-angled polygon with three vertices this point will be inside it, then in an obtuse-angled one - outside it.
Knowing, for example, that one of the sides of an obtuse triangle is equal to its radius, one can find the angle that lies opposite the known face. Its sine will be equal to the result of dividing the length of the known side by 2R (where R is the radius of the circle). That is, the sin of the angle will be equal to ½. So the angle will be 150 o.
If you need to find the radius of the circumscribed circle of an obtuse-angled triangle, then you will need information about the length of its sides (c, v, b) and its area S. After all, the radius is calculated as follows: (c x v x b): 4 x S. By the way, it doesn’t matter what kind of figure do you have: a versatile obtuse triangle, isosceles, right or acute. In any situation, thanks to the above formula, you can find out the area of a given polygon with three sides.
Circumscribed Triangles
It is also quite common to work with inscribed circles. According to one of the formulas, the radius of such a figure, multiplied by ½ of the perimeter, will equal the area of the triangle. True, to find it out, you need to know the sides of an obtuse triangle. Indeed, in order to determine ½ of the perimeter, it is necessary to add their lengths and divide by 2.
To understand where the center of a circle inscribed in an obtuse triangle should be, it is necessary to draw three bisectors. These are the lines that bisect the corners. It is at their intersection that the center of the circle will be located. In this case, it will be equidistant from each side.
The radius of such a circle inscribed in an obtuse triangle is equal to the quotient (p-c) x (p-v) x (p-b) : p. Moreover, p is the half-perimeter of the triangle, c, v, b are its sides.
