In geometry the fundamental terms are point, line, and plane. The line segment is defined with two points for which we say are collinear. Point on a line split the line on two rays or two half-lines. The part of the line that is bounded by two distinct end points is called the line segment. The line segments of equal length are called congruent line segments. The point of the line segments that is equidistant from both ends is called line segment midpoint. The intersection of two lines is the point. The distance between the point and the line is the distance of a normal that is lowered from point on a line. The point where the normal intersects a line is called perpendicular foot.
The plane is defined with three non-collinear points and such points are named coplanar points. If two lines in the planes do not intersect, then these lines are parallel lines. The line in a plane splits the plane on two half-planes. The intersection of two planes is the line. Two mutually parallel planes do not intersect. The angle is part of a plane that is bounded with two half-lines i.e. sides of the angle with common point called vertex of the angle. The point, line, half-line, line segment as well as plane are shown in the following figure.
The angles are measured in degrees and radians. The value of right angle is 90° or \(\left(\frac{\pi}{2} \mathrm{rad}\right)\). The value of straight angle is 180° or \(\pi \mathrm{rad}\) and the value of complete angle is 360° or \(2\pi \mathrm{rad}\). The measure of acute angle is greater than 0° and less than 90°, while the value of obtus angle is greater than 90° and less then 180°. Two angles that have the same measure are congruent angles. If a ray splits the angle on two congruent angles, than this ray is called angle bisector. The sum of two complementary angles is \(\alpha + \beta = 90°\), the sum of two suplementary angles is \(\alpha + \beta = 180°.\)
Two crossed lines splits the plane on four angles as shown in following figure. The neighboring angles, whose sum is 180° are named adjecent angles. These angles are suplemnetary angles. The opposite angles \(\alpha\) and \(\beta\) do not have common arms (half-lines) but they have common vertex of the anlge. These angles are called vertically opposite angles and they are congruent angles (are equal).
If lines \(p\) and \(q\) are parallel, then the line \(k\) which intersects lines \(p\) and \(q\) defines 8 angles as shown in following figure. The angles \(\alpha\) and \(\alpha_1\) are congruent angles. The same is valid for other angles. The line which intersects two or more lines in the same plane is called transversal line.
The plane is defined with three non-collinear points and such points are named coplanar points. If two lines in the planes do not intersect, then these lines are parallel lines. The line in a plane splits the plane on two half-planes. The intersection of two planes is the line. Two mutually parallel planes do not intersect. The angle is part of a plane that is bounded with two half-lines i.e. sides of the angle with common point called vertex of the angle. The point, line, half-line, line segment as well as plane are shown in the following figure.
The angles are measured in degrees and radians. The value of right angle is 90° or \(\left(\frac{\pi}{2} \mathrm{rad}\right)\). The value of straight angle is 180° or \(\pi \mathrm{rad}\) and the value of complete angle is 360° or \(2\pi \mathrm{rad}\). The measure of acute angle is greater than 0° and less than 90°, while the value of obtus angle is greater than 90° and less then 180°. Two angles that have the same measure are congruent angles. If a ray splits the angle on two congruent angles, than this ray is called angle bisector. The sum of two complementary angles is \(\alpha + \beta = 90°\), the sum of two suplementary angles is \(\alpha + \beta = 180°.\)
Two crossed lines splits the plane on four angles as shown in following figure. The neighboring angles, whose sum is 180° are named adjecent angles. These angles are suplemnetary angles. The opposite angles \(\alpha\) and \(\beta\) do not have common arms (half-lines) but they have common vertex of the anlge. These angles are called vertically opposite angles and they are congruent angles (are equal).
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