Разработка практического занятия по теме: «Линии и углы»
Для студентов ЕТК ВГТУ 2 курса технических специальностей.
Цель занятия: развитие профессионально ориентированных уменийустного и письменного общенияпо заданной теме.
Задачи занятия:
- развитие умений просмотрового, изучающего чтения, с извлечением необходимой информации;
- развитие навыков перевода;
- развитие умений обработки информации и вычленения главного из общего;
- развитие и совершенствование лексико-грамматических навыков оформления высказывания по теме;
- развитие навыков письменной речи;
- развитие навыков устой речи;
- развитие мотивационной составляющей за счёт использования текстов общепрофессиональной направленности, актуальной для студентов 2 курса колледжа.
Read the texts. Pay attention to the marked words. Write down Russian equivalents to the italic(?) words andexplain the meaning of the underline words. Make some questions of your own. Be ready to discuss.
Lines
A line is a one-dimensional figure. That is, a line has length, but no width or height. Basically, a line is made up of an infinite number of points. Points in the same line are called colinear. Between each point is another point. This continues on forever. You can never run out of points to discover in a line. However, when you are talking about points as dots, you can get something called a discrete line. A discrete line is a line made up of dots with space between the centers of the dots. A dense line is a line that is the shortest path between two points. The number line, or coordinatized line, is a line where every point is represented by a number and vice versa. The number line is a one-dimensional graph.
If you have two points A and B, the line that contains them is the set of points consisting of the distinct points A and B, all of the points between them, all points for which A is between them and B, and all points for which B is between them and A. A line like that would be written 
. A line can be represented by a single lowercase letter. This is as a contrast to the uppercase letters that represent points. Aline segment is the set of points consisting of A, B, and all points between them. A line segment is written 
. If you have two points A and B, the ray that contains them is the set of points consisting of the distinct points A and B, all of the points between them, and all points for which B is between them and A. This is written 
.
Every line is either horizontal, vertical or oblique. Horizontal and vertical speak for themselves, and an oblique line is any line that isn't horizontal or vertical. Horizontal lines have a slope of zero. Vertical lines are said to have infinite slope, because they just go straight up and not over. People just can't stand that zero in the denominator. In space, vertical lines never meet (they just go straight up/down), but it is possible for horizontal lines.
There are four different relationships that two lines can have. Lines can be identical, intersecting, parallel, perpendicular, or skew. Identical lines are lines that coincide. Therefore, they are the same line. The second one is the most obvious. Intersecting lines are lines that share a point. Parallel lines are coplanar lines that never intersect. They always have a certain distance between them and always have the same direction. Perpendicular lines are lines that intersect in one point and form a 90 degree angle while they're at it. Skew lines only happen in space. They are noncoplanar lines that never intersect. Unlike parallel lines, however, they don't always have a set distance between them, nor do they always have the same direction.
Planes
Planes are two-dimensional. A plane has length and width, but no height, and extends infinitely on all sides. Planes are thought of as flat surfaces, like a table top. A plane is made up of an infinite amount of lines. Two-dimensional figures are called plane figures. While this really should be in Algebra, coordinate planes are two-dimensional graphs that use the ordered pair to locate points. Another name for coordinate planes are Cartesian planes.
Space
Space is the set of all points. It is made up of an infinite number of planes. Figures in space are called solids or surfaces. Coordinate space uses three coordinates. Instead of an ordered pair, an ordered triple is used. The new variable, z, measures the distance forwards or backwards that you move. The ordered triple looks like this: (x, y, z). You might see more on space and 3-D figures later, in a different section.
Explain to your teacher what 3-D means.
A line is a group of points on a straight path that extends to infinity.
Any two points on the line can be used to name it. This line is called line DE.
| Aline segmentis a part of a line that has two end points. 
The two end points of the line segment are used to name the line segment. This line segment is called segment XY. 
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| A ray is part of a line. It has one end point and extends to infinity in one direction. A ray is named starting with its end point first and then any other point on the ray second. |
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| Using the graphic to the left:Name a line: Name a line segment with U as an end point: Name a ray with V as an end point: |
Transversals
A transversal, or a line that intersects two or more coplanar lines, each at a different point, is a very useful line in geometry. Transversals tell us a great deal about angles. There is a special rule used in geometry (the Transversal Postulate) that involves angles and transversals. It says that if two parallel lines are intersected by a transversal, then the corresponding angles are congruent.
Example. 1. Given: r is parallel to s angle 1 = 60 degrees Find the measures of the other seven angles in the accompanying figure (below).
Solution: Angle 2 = 120 degrees since it is supplementary to angle 1. Supplementary angles are any two angles whose sum is 180 degrees. Angle 3 = 60 degrees since Angle 1 and Angle 3 are vertical angles. ertical angles are two nonadjacent angles formed by two intersecting lines. Angle 4 = 120 degrees since it is supplementary to angle 1. Angle 5 = angle 1 by the Transversal Postulate. Angle 6 = angle 2, angle 7 = angle 3, and angle 8 = angle 4 by the Transveral Postulate.