Points and lines

Geometry is the branch of mathematics which investigates the relations, properties and measurements of solids, surf aces, lines and angles.

A line has no width or thickness. It has length and direction. An infinite number of straight lines can be drawn through one point. Since a line extends indefinitely in either direction, we must work with line segments, or portions of lines.

A line joins two points. The two points may be at any distance apart, so a straight line may be considered as having any length. Only one straight line can be drawn between two points. There are three kinds of lines: straight, curved and broken.

A broken line is a line formed of successive sections, or segments, of straight lines.

A curved line, or simply a curve, is a line no portion of which is straight.

A point has no length, width or thickness. It simply indicates position.

Lines that extend from left to right as the horizon are called horizontal lines. Examples of horizontal lines are lines on writing paper and all level lines which we find in man-made structures.

NOTE:

man-made structures - постройки и сооружения, созданные руками человека

Exercises:

1. Read the following words paying attention to the pronunciation: length, thickness, width, straight, draw, curve, position, representation, either, more.

2. Give Russian equivalents to the following:

simply indicates position, infinitive number of straight lines, extend from left to right, may be considered as having smth., a line no potion of which is straight, measurements of solids, at any distance apart, successive section.

3. Form nouns adding suffixes and translate the newly formed words into Russian:

- tion: construct, represent, multiply, form;

- ment: displace, measure;

- ing: draw, study, find.

4. Answer the following questions:

1. What are the characteristic features of a point?

2. How many lines can be drawn through one point?

3. What is a segment?

4. How many lines can be drawn between two points?

5. What kind of lines do you know?

5. Read and translate the text. Retell it.

Solid geometry

Two planes (both conceived as indefinitely extended) may have three situations relative to each other:

(a) they may coincide throughout their whole extent;

(b) they may intersect, in which case the inter­section is a line;

(c) they may never intersect, in which case they are parallel.

A plane is perpendicular to another plane when the straight lines drawn in either of the planes perpendicular to the common section of the two planes are perpendicular to the other plane.

(It is here assumed that the common section of the two planes is a straight line).

6. Translate into English:

Через любые две точки можно провести прямую и притом только одну. Существует три типа линий: прямая, кривая и ломаная. Линии не имеют ширины и толщины, но имеют длину и направление. Через одну точку можно провести бесконечное количество линий.