Perhaps the most basic, simple and interesting figure in geometry is a triangle.In the course of high school study its main properties, but sometimes knowledge on the subject incomplete form.Types of triangles initially determine their properties.But such a view remains mixed.So now we analyze a little more about it.
Types of triangles depend on the degree measure of angles.These figures are ostro-, straight-and obtuse.If all the angles do not exceed the value of 90 degrees, 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 under consideration geometric figure called obtuse.
There are many tasks for the acute-angled subspecies.A distinctive feature is the internal location of the points of intersection of bisectors, medians and altitudes.In other cases, this condition can not be satisfied.Identify the type of "triangle" figure difficult.It suffices to know for example, the cosine of each angle.If any value is less than zero, it means that in any case the triangle is obtuse.In the case of the zero index figure has right angles.All positive values ​​guaranteed prompt you that in front of you an acute-angled view.
can not say about the right triangle.It is the most ideal form, where all the points of intersection coincide medians, bisectors and altitudes.Center of inscribed and circumscribed circle lies in one place.To solve the problems you need to know only one side, as you initially set angles, the other two sides are known.That is the figure given by only one parameter.There are isosceles triangles.Their main feature - the equality of the two sides and angles at the base.
Sometimes there is a question about whether there is a triangle with a given side.In fact, you are asking whether this is suitable for the description of the main types.For example, if the sum of the two sides is less than a third, 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 3,5,9, there is an obvious trick.This can be explained without complex mathematical techniques.Suppose you want to get from point A to point B. The distance in a straight line is 9 kilometers.However, you are reminded that you must go to point C in the store.The distance from A to C is 3 kilometers away, and from C to B - 5. Thus it turns out that, moving through the store, you will pass on less than one kilometer.But since the point C is located on the straight line AB, then you have to go the extra distance.There is a contradiction.This, of course, conventional explanation.Mathematics knows no one way to prove that the triangles are subject to all kinds of basic identity.It states that the sum of two sides longer than the third.
Any kind has the following properties:
1) The sum of all the angles equals 180 degrees.
2) There is always the orthocenter - the point of intersection of the three altitudes.
3) All three of the median drawn from the vertex of the interior angles intersect in one place.
4) around any triangle can be described as a circle.You can also enter the circle so that he had only three points of contact and do not go outside.
Now you acquainted with the basic properties, which have different types of triangles.In the future, it is important to understand what you're dealing with the solution of the problem.
