Types of triangles, angles and sides

Perhaps the most basic, simple and interesting figure in geometry is the triangle. In the course of secondary school its basic properties are studied, however sometimes knowledge on this topic is formed incomplete. Types of triangles initially determine their properties. But this idea remains mixed. So now let's take a closer look at this topic.

The types of triangles depend on the degree measure of the angles. These figures are sharp, straight and obtuse. If all the angles do not exceed a value of 90 degrees, then the figure can be safely called acute. If at least one corner of the triangle is 90 degrees, then you are dealing with a rectangular subspecies. Accordingly, in all other cases, the geometrical figure in question is called obtuse.

There are many problems for acute-angled subspecies. A distinctive feature is the internal location of intersection points of bisectors, medians and heights. In other cases this condition may not be fulfilled. Determine the type of the figure "triangle" is not difficult. It is enough to know, for example, the cosine of each corner. If any values are less than zero, then the triangle is in any case obtuse. In the case of zero index, the figure has a right angle. All positive values are guaranteed to tell you that you have an acute-angled view.

It is impossible not to say the right triangle. This is the most ideal view, where all the intersections of medians, bisectors and heights coincide. The center of the inscribed and circumscribed circle lies also in one place. To solve problems it is necessary to know only one side, since you have angles initially set, and the other two sides are known. That is, the figure is specified by only one parameter. There are isosceles triangles. Their main feature is the equality of two sides and angles at the bottom.

Sometimes the question is whether there is a triangle with given sides. In fact, you are asked whether this description is suitable for the main species. For example, if the sum of the two sides is less than the third, then in reality such a figure does not exist at all. If the job is asked to find the cosines of the angles of a triangle with sides of 3.5.9, then here is an obvious trick. This can be explained without complex mathematical methods. Suppose you want to get from point A to point B. The distance in a straight line is 9 kilometers. However, you remembered that you need to go to point C in the store. The distance from A to C is 3 km, and from C to B - 5. Thus it turns out that moving through the store, you will pass one kilometer less. But since point C is not located on the line AB, then you have to go the extra distance. Here there is a contradiction. This, of course, is a conditional explanation. Mathematics knows not one way of proving that all kinds of triangles obey the basic identity. It says that the sum of the two sides is greater than the length of the third.

Any species has the following properties:

1) The sum of all angles is 180 degrees.

2) There is always an orthocenter - the point of intersection of all three heights.

3) All three medians drawn from the vertices of interior angles intersect in one place.

4) A circle can be described around any triangle. You can also enter a circle so that it has only three points of contact and does not go beyond the outer sides.

Now you are introduced to the basic properties that different kinds of triangles have. In the future it is important to understand what you are dealing with when solving a problem.