Even preschool children know what a triangle looks like. But the kids are already starting to understand what they are like at school. One type is an obtuse triangle. The easiest way to understand what it is is to see a picture of it. And in theory this is what they call the “simplest polygon” with three sides and vertices, one of which is
Understanding the concepts
In geometry, there are these types of figures with three sides: acute, right and obtuse triangles. Moreover, the properties of these simplest polygons are the same for all. Thus, for all listed species this inequality will be observed. The sum of the lengths of any two sides will necessarily be 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 equal to 180 degrees. The same is true for other types of figures with three sides. True, in an obtuse triangle, one of the angles will be even greater than 90°, and the remaining two will certainly be acute. In this case, it is the largest angle that will be opposite the longest side. True, these are not all the properties of an obtuse triangle. But even knowing only these features, schoolchildren can solve many problems in geometry.
For every polygon with three vertices, it is also true that by continuing any of the sides, we obtain 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 this, mathematicians have developed various formulas, depending on what data is initially present.
Correct style
One of the most important conditions for solving geometry problems is the correct drawing. Mathematics teachers often say that it will help not only to visualize what is given and what is required of you, but to get 80% closer to the correct answer. This is why it is important to know how to construct an obtuse triangle. If you just need 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 triangle in accordance with them. In this case, it is necessary to try to depict the angles as accurately as possible, calculating them using a protractor, and display the sides in proportion to the conditions given in the task.
Main lines
Often, it is not enough for schoolchildren to know only what certain figures should look like. They cannot limit themselves to information only about which triangle is obtuse and which is right. The mathematics course requires that their knowledge of the basic features of figures should be more complete.
So, every schoolchild should understand the definition of bisector, median, perpendicular bisector and height. In addition, he must know their basic properties.
Thus, bisectors divide an angle in half, and the opposite side into segments that are proportional to the adjacent sides.
The median divides any triangle into two equal in area. At the point at which they intersect, each of them is divided into 2 segments in a 2: 1 ratio, when viewed from the vertex from which it emerged. In this case, the large median is always drawn to its smallest side.
No less attention is paid to height. This is perpendicular to the side opposite the corner. The height of an obtuse triangle has its own characteristics. If it is drawn from a sharp vertex, then it does not end up on the side of this simplest polygon, but on its continuation.
The perpendicular bisector is the line segment that extends from the center of the triangle's face. Moreover, it is located at a right angle to it.
Working with circles
At the beginning of studying geometry, it is enough for children to understand how to draw an obtuse triangle, learn to distinguish it from other types and remember its basic properties. But for high school students this knowledge is no longer enough. For example, on the Unified State 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 triangle is much more difficult, because to do 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 them to determine their location as accurately as possible.
Inscribed triangles
As stated earlier, if a circle passes through all three vertices, then it is called a circumcircle. Its main property is that it is unique. To find out how the circumscribed circle of an obtuse triangle should be located, you need to remember that its center is at the intersection of the three bisectoral perpendiculars that go to the sides of the figure. If in an acute-angled polygon with three vertices this point will be located inside it, then in an obtuse-angled polygon it will be outside it.
Knowing, for example, that one of the sides of an obtuse triangle is equal to its radius, you 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. This means that the angle will be equal to 150°.
If you need to find the circumradius of an obtuse 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 like this: (c x v x b) : 4 x S. By the way, it doesn’t matter , what type of figure you have: a scalene obtuse triangle, isosceles, right- or acute-angled. In any situation, thanks to the above formula, you can find out the area of a given polygon with three sides.
Circumscribed triangles
You also often have to work with inscribed circles. According to one formula, the radius of such a figure, multiplied by ½ the perimeter, will be equal to the area of the triangle. True, to figure it out you need to know the sides of an obtuse triangle. After all, in order to determine ½ the perimeter, you need 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. In this case, p is the semi-perimeter of the triangle, c, v, b are its sides.
How to draw a triangle?
Construction of various triangles is a mandatory element of the 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 midpoint 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:
