EXERCISES. I. Read the following words paying attention to the pronun­ciation:

I. Read the following words paying attention to the pronun­ciation:

length, thickness, width, thin, straight, draw, through, curve, there, that, position, representation, profession, either, or, more.

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

-tion: construct, represent, multiply, form;

-ment: displace, measure;

-ing: draw, study, find.

III. Make up sentences of your own using the words and ex­pressions given below:

daily work, closed figures, to be represented by, thickness to extend, indefinitely, labeled by, a broken line.

IV. Answer the following questions:

1. What is geometry? 2. What are the characteristic fea­tures of a point? 3. How do We represent a point in geometry? 4. How many lines can be drawn through one point? 5. What is a segment? 6. How many lines can be drawn between two points? 7. What kind of lines do you know?

V. Translate into Russian:

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

The two points may be at any distance apart, so a straight line may be considered as having any length.

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.

VI. Translate into English:

Через любые две точки можно провести прямую и при­том только одну. Если на плоскости взять какие-нибудь две точки и провести через них прямую линию, то все точки этой прямой будут находиться в этой плоскости.

TEXT

ANGLES

Measuring Angles. An angle is formed when two straight lines meet at a point. The lines are called the sides of an angle. The point at which the sides meet is called the vertex of the angle. The angle is read as angle BAC or CAB (Fig. 4).

The size of an angle depends upon¹ the amount one side has turned away from² the other. The length of the sides of an angle does not determine its size.

The unit of measure used in measuring an angle is the de­gree. A degree is a unit that equals 1/90 of a right angle and 1/360 of a circle. A right angle, therefore, contains 90 degrees (90°), and a circle contains 360 degrees (360°). The size of an angle is the number of degrees through which one side of the angle has turned away from the other side. Kinds of Angles.

Right Angle. If one side of an angle turns a quarter of a complete circle away from the other side, the angle that is formed is a right angle (Fig. 5). It contains 90°.

When two lines intersect at right angles, the lines are per­pendicular Each angle formed by a perpendicular line con­tains 90° (Fig. 6).

Complementary angles. When two angles put together form a right angle, and thus their sum is 90°, the angles a№ complementary. For example, angle DBC is the complemen­tary of angle ABC since their sum (60°+30°) equals 90° (Fig. 7).

Straight Angle. If one side of an angle turns half a comple­te circle away from the other side, the angle that is formed is a straight angle (Fig. 8). The sides of a straight angle lie in the same straight line. Notice _A that a straight angle is twice the size of³ a right angle since in a straight angle the side has made half a complete turn,⁴ or two quarter turns. The num­ber of degrees in a straight angle is miJ

Supplementary Angles. When the sum of two angles is 180°, the angles are said to be⁵ supplementary. For example, angle ABC is the supple­mentary angle of angle CBD since their sum (120^a+60°) is 180° (Fig. 9).

Acute Angle. If one side of an angle turns less than a quarter of a circle away from the other side, the angle formed is an acute angle (Fig. 10). An acute angle, therefore, is smaller than a right angle, or less than 90°.

Obtuse Angle. If one side of an angle turns more than a quarter of a circle but less than half a circle away from the other side, the angle formed is an obtuse angle (Fig. 11). Therefore, an obtuse angle is greater than a right angle but smaller than a straight angle. It contains more than 90º but less than 180°.

Reflex Angle. If one side of an angle turns more than half

a circle (180°) but less than a complete circle (360°) away from the other side, the angle formed is a reflex angle (Fig. 12). Therefore, a reflex angle is greater than A straight angle.

Notes:

¹to depend upon — зависеть от

²has turned away from — отклонен от

³twice the size of — вдвое больше (по величине)

⁴half a complete turn — половину полного оборота

⁵angles are said to be — про углы говорят, что они (являются)