Even pre-school children know, it looks like a triangle.But so what they are, the guys are already beginning to understand the school.One type is an obtuse triangle.Understand what it is easiest to see if the picture with his image.In theory, this so-called "simple polygon" with three sides and tops, one of which is an obtuse angle.
are investigated with the concepts in geometry
distinguish these types of figures with three sides: acute-angled, rectangular, obtuse-angled triangle.The properties of these simple polygons are the same for everyone.So, for all these species will be observed this inequality.The sum of the lengths of any two sides is bound to be more than the length of a third party.
But in order to be sure that we are talking about a complete figure, rather than a set of individual nodes, you must check to comply with the basic requirement that the sum of angles of a triangle is equal to 180 ° obtuse.The same is true for other types of figures with three sides.However, in an obtuse triangle one of the angles will be more 90 degrees, and the remaining two are bound to be sharp.When this is the largest angle will be opposite the longest side.However, this is not all features of an obtuse-angled triangle.But just knowing these features, students can solve many problems in geometry.
For each polygon with three vertices is also true that, while continuing to either side, we get the angle, the size of which will be equal to the sum of two non-contiguous with it internal vertices.Perimeter obtuse triangle is calculated in the same way as for other figures.It equals the sum of the lengths of all its sides.To determine the area of the triangle mathematicians were withdrawn different formulas, depending on what data is present initially.
correct mark
One of the most important conditions for solution of problems in geometry is the correct figure.Most math teachers say that it will help not only to visualize what is given and what is required of you, but 80% closer to the correct answer.It is therefore important to know how to build an obtuse triangle.If you need just a hypothetical figure, you can draw any polygon with three sides, so that one of the angles of 90 degrees was bigger.
If certain values are lengths of the sides or corners of degrees, it is necessary to draw an obtuse triangle in accordance with them.It is necessary to try to portray as accurately as possible the angles, calculating them with a protractor, and proportionally according to the conditions in the job display side.
main line
students often enough to know just how you like those or other figures.They can not limit ourselves to information about how obtuse triangle and a rectangle.Mathematics course provided that their knowledge of the basic features of the figures should be more complete.
So, each student should be clear definition of bisector, median, and the perpendicular height.In addition, he needs to know their basic properties.
Thus, the angle bisector divided in half, and the opposite direction - into segments that are proportional to the adjacent sides.
median divides any triangle into two equal areas.At the point where they intersect, each of which is partitioned into two lengths in the ratio 2: 1, as viewed from the top, from which it came.This large media always held to its lower side.
No less attention is paid to the altitude.This perpendicular angle to the opposite side.Height obtuse triangle has its own characteristics.If it is done from the acute vertex, then it hits not on the side of the simple polygon, and in its continuation.
midperpendicular - a segment that goes from the center of the triangle faces.He located it at a right angle.
Working with circles
At the beginning of the study of the geometry of the children enough to understand how to draw an obtuse triangle, learn to distinguish it from other species, and remember its basic properties.But high school students that knowledge is not enough.For example, exam Frequently asked questions about the circumscribed and the inscribed circle.The first relates to the three vertices of the triangle, and the other has a common point with all parties.
Construct the inscribed or circumscribed obtuse triangle has much more difficult, because it requires to begin to figure out where you want the center of the circle and its radius.By the way, will be an essential tool in this case is not only a pencil with a ruler, but also a compass.
same difficulties arise in constructing the inscribed polygon with three sides.Mathematics were derived various formulas that allow us to determine their location as accurately as possible.
Inscribed triangles
As mentioned earlier, if a circle passes through all three vertices, it is called the circumscribed circle.Its main feature is that it is unique.To find out how to be positioned circle described obtuse-angled triangle, we must remember that its center is located at the intersection of three midperpendiculars that go to the side of the figure.If an acute-angled polygon with three vertices, this point will be located inside it, the obtuse - beyond.
Knowing, for example, that one of the parties obtuse-angled triangle is equal to its radius, it is possible to find an angle that lies opposite the famous faces.His sin is equal to the result obtained by dividing the length of the well-known side to the 2R (where R - the radius of the circle).That is the sin of the angle is equal to ½.Hence, the angle is equal to 150 °.
If you need to find the radius of the circle obtuse triangle, you useful information on the length of its sides (c, v, b) and radius of the area S. It is calculated as follows: (c x v x b): 4 x S. By the way, no matter what it is you kind of figure: a versatile obtuse triangle, isosceles, acute-angled straight-or.In any situation, thanks to this formula, you can learn a given area of a polygon with three sides.
described triangles
also often have to work with the inscribed circles.According to one of the formulas, the radius of the figure, ½ multiplied by the perimeter will be equal to the area of a triangle.However, for her clarification you need to know the part of obtuse triangle.After all, in order to determine ½ perimeter, it is necessary to lay down their length and divide by 2.
To understand where you want the center of the circle inscribed in the triangle is obtuse, it is necessary to spend three bisector.This is the line that divides the corners in half.It is at their intersection and will be the center of the circle.At the same time it will be equidistant from each of the parties.
radius of a circle inscribed in the obtuse-angled triangle is equal to the square root of the private (pc) x (pv) x (pb): p.Wherein p - is semiperimeter triangle, c, v, b - side of it.
