A triangle is a geometric figure that has three points connected by lines that do not lie on a single straight line in a plane. The vertices of a triangle are the points at the base of the corners, and the lines connecting them are called the sides of the triangle. To determine the area of such a figure, the interior space of a triangle is often used.
Classification
In addition to triangles with unequal sides, there are isosceles triangles, that is, having two identical sides. They are called side, and another side is the base of the figure. There is another type of such polygons - equilateral. All three sides are the same length.
Triangles have a degree measurement system. These figures can have different angles, so they are classified as follows:
- Rectangular - having an angle of 90 degrees. The two sides adjacent to this angle are called the legs, and the third is called the hypotenuse;
- Acute triangles are triangles that have all acute angles not exceeding 90degrees;
- Obtuse - one angle greater than 90 degrees.
Definition and parameters of a triangle
As already noted, a triangle is one of the types of polygons that has three vertices and the same number of lines connecting them. The lines are usually denoted in the same way: the corners are in small Latin letters, and the opposite sides of each are in the corresponding capital letter.
If you add up all the angles of a triangle, you get the sum of 180 degrees. To find out the inner angle, you need to subtract the outer angle of the triangle from 180 degrees. In order to find out what the outside angle is equal to, it is worth adding the two inside angles separated from it.
In each triangle, whether it has acute or obtuse angles, the largest side is opposite to the large angle. If the lines between the vertices are the same, then, respectively, each angle is equal to 60 degrees.
Obt-angled triangle
An obtuse angle of a triangle is always greater than a 90-degree angle, but less than a straight angle. Thus, an obtuse angle is between 90 and 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 1800. If two angles are, for example, 95 degrees each, then there is simply no place for the third one.
Two obtuse polygons are equal:
- if both their sides and the angle between them are equal;
- if one side and two corners,adjacent to it are equal;
- if three sides of obtuse triangles are equal.
Remarkable obtuse triangle lines
In all triangles with obtuse angles, there are lines called wonderful. The first one is height. It is a perpendicular from one of the vertices to the corresponding side. All heights collide at a point, which is referred to as the orthocenter. In a triangle with obtuse angles, it will be outside the figure itself. As for sharp corners, the center there is in the triangle itself.
One more 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.
Bisector - a line dividing in half both obtuse angles and the rest. The intersection of three such lines always occurs only in the figure itself and is defined as the center of a circle inscribed in a triangle.
In turn, the center of the circle described around the figure can be obtained from the three median perpendiculars. These are lines that have been dropped from the midpoints of the lines connecting the vertices. The intersection of the three median perpendiculars in a triangle with obtuse angles is outside the figure.
