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MEDIAN, the height and properties and their bisector

Median height and bisector and their properties

Research Triangle occupied mathematicians for centuries.

Most of the properties and theorems relating to triangles, using special line figures: median, bisector and altitude.

Median and properties

The median - this is one of the main lines of the triangle. This segment and the line on which it lies, connects the point at the head of the angle of the triangle to the middle of the opposite side of the same figure. In an equilateral triangle, the median is also bisector and altitude.
Property medians, which will greatly facilitate thesolution of many problems, is as follows: if the median of a triangle hold each corner, they all intersect at one point, will be divided in the ratio 2: 1. The ratio should be measured from the vertex of the angle.
The median has the ability to share everything equally. For example, any median divides into two other triangle equal to its area. And if you spend all three medians, the more triangles will turn 6 small, as equal in size. These figures (the same area) are the equal of.


Bisector represents a beam thatIt begins at the vertex of the angle and divides in two the same angle. The points on this ray, equidistant from the sides of the angle. Properties bisector well help in solving the problems related to triangles.
In triangle the bisector of a segment called,which lies on the bisector of the angle beam and connects with the opposite side of the top. The point of intersection with the side divides it into segments whose ratio is the ratio of the adjacent sides to them.
If inscribe a circle in a triangle, itscenter will coincide with the point of intersection of the bisectors of the triangle. This property is reflected in solid geometry - it plays the role of a triangle pyramid, and the circle - ball.


Also, as the median bisector and height infirst triangle vertex angle and connect the opposite side. This relationship arises as follows: height - is the perpendicular drawn from the vertex to the line that contains the opposite side.
If the height is held in a right triangle, it touching the opposite side, it divides the triangle into the other two, which in turn are similar to the first.
Often the term is used in the perpendicularsolid geometry to determine the relative position of the lines in different planes and the distance between them. In this case the segment performing the function of the perpendicular must have a right angle with the two straight lines. Then the numeric value of this segment will show the distance between the two figures.

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