Basic notions in geomerty

author: Петя
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Българска версия:

   For basic notions in geometry are point, a line and a plane.

§ An axis is called a line with a positive direction over it.

§ If point O lies on a straight line, then the point divides the line on two parts, each of which is called a ray with initial O.

These rays are called contrary  rays.

§  Each line р from а fixed plane, divides it into two parts, each of which are called a half-plane with outline - line р.

§ A part from a line, limited by two points, is called a segment.

Points, limiting a segment, are called ends of the segment. Every other point from the segment is called an interior point.

§ A length of a segment is called a positive number, which is getting from its gauged with a chosen a linear measure.

A length on a segment АВ is marked  |АВ| or just АВ.

§   A distance between two points is called a length on the segment, definite by them.

§ Two segments are called equal if their lengths, gauged with one linear measure, are equal.

An axiom for synonymous drawing on a segment over a ray: If two equals segments are drawing over a ray then their ends  tallied.

§ We say that the segment а is bigger (smaller) then the segment b, if the length of  а is bigger (smaller) than the length of b.

§   If point М is between the points А and В and АМ=МВ, then М is called a midpoint of the segment АВ.

§ If а and b are segments, then if ОА=а and АВ=b, we say that the segment ОВ=с is a sum of segments а and b.

If one segment is a sum of two or more given segments, then its length is equal to the sum of the lengths on the given segments.

§  The difference between two segments а and b (a>b) is called a segment d, whichsum with segment b is equal on а.

We mark:  d=a-b

§ A geometric figure which is consist of two rays with common start, is called an angle.

The two legs are called rays of the angle, and its common start - a vertex of the angle.

An angle which half-planes are contrary rays, is called straight angle.

§ Interior points of an angle АОВ are called common points of the two half-plane:

l - with contour ОА, which contains point В, and

m - with contour line ОВ, which contains point  А.

If X is an interior point for the angle АОВ, the line ОХ is called an interior line for the angle АОВ.

§        Measure of an angle is called a positive number, obtained by measuring the angle with a chosen angle measure.

§        Angle measures for 1 degree and its partition:
a)    One degree: 1° is 1/180 part of the straight angle;
b)   One minute: 1^' is 1/60 of 1°;
c)    One second: 1'' is 1/60 of 1^', which is1/3600 of1°;
d)  Other..

      Two angles are equal if they have equal measures.

An axiom for synonymous drawing of an angle: If two equal angles with a common ray are drawn in one plane with contour this common ray, then their second legs tallied.

§ From two angles bigger (smaller) is the one which has bigger (smaller) measure.

§An angle bisector is called the ray with a start - the vertex of the angle, that divides this angle on two equal angles.

Sometimes the line which lies on the angle bisector on a given angle, is called an angle bisector of this angle.

If a and b are two angles
A sum of the angles a and b:angle АОВ =a and angle ВОС = b, then angle АОС =a + b
A difference on angles  a and b: angle АОВ =a and angle АОС = b,then angle  ВОС = a - b