Straight lines which are not crossed are considered as parallel and lie on one plane. If straight lines do not lie in one plane and are not crossed, call them crossed. It is possible to prove parallelism of straight lines, proceeding from their properties. It can be done, doing direct measurements.
It is required to you
- - ruler;
- - protractor;
- - square;
- - calculator.
Instruction
1. Before the proof make sure that straight lines lie in one plane and they can be represented on it. The easiest way of the proof is the measurement method a ruler. For this purpose by means of a ruler measure distance between straight lines in several places as it is possible further from each other. If the distance remains invariable, these straight lines are parallel. But such method is insufficiently exact therefore use other methods better.
2. Draw the third straight line so that it crossed both parallel straight lines. It forms with them four external and four internal corners. Consider internal corners. Those which lie through a secant direct are called nakrestlezhashchy. Those that about one party lies are called unilateral. By means of a protractor measure two internal nakrestlezhashchy corners. If they are equal among themselves, then straight lines will be parallel. If there were doubts, measure unilateral internal corners and put the turned-out values. Straight lines will be parallel if the sum of unilateral internal corners is equal 180º.
3. If there is no protractor, take the square with a corner 90º. With its help construct a perpendicular to one of straight lines. After that continue this perpendicular so that it crossed other straight line. By means of the same square check under what corner this perpendicular crosses it. If this corner is equal 90º too, then straight lines are parallel among themselves.
4. In case straight lines are set in the Cartesian system of coordinates, find their guides or normal vectors. If these vectors, respectively, among themselves kollinearna, then straight lines are parallel. Lead the equation of straight lines to a general view and find coordinates of a normal vector of each of straight lines. Its coordinates are equal to coefficients And yes Century. In case the relation of the corresponding coordinates of normal vectors is identical, they are kollinearna, and straight lines are parallel.
5. For example, straight lines are set by the equations to a 4kh-2 +1=0 and x / 1= (at-4)/2. The first equation – a general view, the second – initial. Lead the second equation to a general view. Use for this purpose the rule of transformation of proportions, as a result receive the 2nd = at-4. After reduction to a general view receive 2kh-at +4=0. As the equation of a general view for any straight line registers Ah + Wu + C=0, for the first straight line: And =4, V =2, and for the second direct A=2, B =1. For the first direct coordinate of a normal vector (4;2), and for the second – (2;1). Find the relation of the corresponding coordinates of normal vectors 4/2=2 and 2/1=2. These numbers are equal, so a kollinearna vector. As kollinearna vector, straight lines are parallel.