Dull angles: description and features

A triangle is a geometric figure that has three points connected by lines that do not lie on a single straight line in the plane. The vertices of the triangle are the points at the base of the corners, and the lines joining them are called the sides of the triangle. To determine the area of such a figure, often use the inner space of the triangle.

Classification

In addition to triangles with unequal sides, there are isosceles, that is, possessing two identical sides. They are called lateral, and one side is the base of the figure. There is another kind of such polygons - equilateral. All three sides have the same length.

For triangles, there is a degree system of measurement. 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 corner are called katetas, and the third - hypotenuse;
• Sharp-angled ones are triangles with all sharp angles not exceeding 90 degrees;
• Obtuse-angled - one angle greater than 90 degrees.

Definition and parameters of a triangle

As already noted, the triangle is one of the types of polygons that has three vertices and the same number of straight lines that unite them. Denote the lines, as a rule, the same: the angles - in small Latin letters, and the opposite sides of each - the corresponding large letter.

If you add all the angles of a triangle, you get the sum of 180 degrees. To know the inner corner, you need from 180 Degrees subtract the value of the outer corner of the triangle. In order to find out what the angle that is on the outside equals, it is necessary to add two separate angles from it inside.

In each triangle, it has sharp or obtuse angles, opposite to the large angle is the largest side. If the lines between the vertices are the same, then, respectively, and each angle is equal to 60 degrees.

The obtuse triangle

The obtuse angle of the triangle is always greater than the 90-degree angle, but less than the 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 should be less than 180 ⁰ . If two angles have, for example, 95 degrees, then the third one simply does not have a place.

Two obtuse-angled polygons are equal:

• If both sides are equal and the angle between them is equal;
• If one side and two angles adjacent to it are equal;
• If three sides of obtuse triangles have equality.

Wonderful lines of the obtuse triangle

In all triangles with obtuse angles, there are lines called remarkable. The first of them is the 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 the sharp corners, the center there is in the triangle itself.

Another line is the median. This is a trait drawn from the top to the center of the corresponding side. All medians converge in the triangle, and the place of their alignment is the center of gravity of such a polygon.

Bisectrix - a line dividing in half like 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 a circle inscribed in a triangle.

In turn, the center of the circle described around the figure can be obtained from three middle perpendiculars. These are the lines that have been omitted from the middle of the straight lines that connect the peaks. The intersection of three medial perpendiculars in a triangle having obtuse angles is located outside the figure.