A triangle is a geometric figure that has three points connected to each other by lines that do not lie on a single straight line in the plane. The vertices of a triangle are the points at the base of the angles, and the lines connecting them are called the sides of the triangle. To determine the area of such a figure, the interior of the triangle is often used.
Classification
In addition to triangles having unequal sides, there are isosceles, that is, having two identical sides. They are called side, and another side - the base of the figure. There is another type of such polygons - equilateral. All three of their sides have the same length.
For triangles, a degree measurement system is inherent. These figures can have different angles, so they are classified as follows:
- Rectangular - having an angle of 90 degrees. Two sides adjacent to this corner are called legs, and the third is called hypotenuse;
- Angular - these are triangles with all sharp angles not exceeding 90 degrees;
- Obtuse - one angle is greater than 90 degrees.
Definition and parameters of a triangle
As already noted, a triangle is a type of polygon that has three vertices and as many straight lines that unite them. The lines are usually marked the same way: the corners in small Latin letters, and the opposite sides of each in the corresponding capital letter.
If you add up all the corners of a triangle, you get a sum of 180 degrees. To find out the internal angle, you need from 180 degrees, subtract the value of the external angle of the triangle. In order to find out what is the angle that is outside, it is worth folding two separate angles from it inside.
In each triangle, it has sharp or obtuse angles, the opposite side is the largest side. If the straight lines between the vertices are the same, then, accordingly, each angle is 60 degrees.
Obtuse triangle
The obtuse angle of a triangle is always greater than a 90-degree angle, but less than an unfolded angle. Thus, the obtuse angle is from 90 to 180 degrees.
The question arises: is there more than one obtuse angle in such a figure? The answer is on the surface: no, because the sum of the angles must be less than 180 0 . If two angles are, for example, at 95 degrees, then the third simply cannot be found.
Two obtuse polygons are equal:
- if both sides are equal and the angle between them is equal;
- if one side and two corners located next to it are equal;
- if the three sides of obtuse triangles have equality.
Wonderful lines of an obtuse triangle
In all triangles having obtuse angles, there are lines called wonderful. The first one is height. It is a perpendicular from one of the vertices to the side corresponding to it. All heights collide at a point called an orthocenter. In a triangle with obtuse angles, it will be located outside the shape itself. As for sharp corners, the center there is in the triangle itself.
Another line is the median. This is a line drawn from the top to the center of the corresponding side. All medians converge in a triangle, and the place of their combination is the center of gravity of such a polygon.
The bisector is a line that bisects both obtuse angles and the rest. The intersection of three such lines always happens only in the figure itself and is defined as the center of the circle inscribed in the triangle.
In turn, the center of the circle circumscribed around the figure can be obtained from the three middle perpendiculars. These are the lines that were dropped from the midpoints of the lines connecting the vertices. The intersection of the three middle perpendiculars in a triangle having obtuse angles is located outside the figure.