II. Match the terms from the left column and definitions

from the right column:

 

an angle	formed by, or with reference to, a straight line or plane perpendicular to a base
null	of less than 90 degrees
right	designating an angle greater than a straight angle (180 degrees)
obtuse	height above a surface, as of the earth
flat	the shape made by two straight lines meeting at a com­mon point, the vertex, or by two planes, meeting along an edge
acute	a decrease in force, activity, amount, etc. - a decrease in force, activity, amount, etc.
reflex	greater than 90 degrees and less than 180 degrees greater than 90 degrees and less than 180 degrees
elevation	designating of, or being zero, as: a) having all zero ele­ments (null matrix), b) having a limit of zero (null se­quence), c) having no members whatsoever (null set)
depression	absolute, positive

III. Give the Russian equivalents of the following words and word combinations:

 

1. side (arm)

2. acute angle

3. angle of depression

4. direction angle

5. sense of rotation

6. clockwise sense

7. vertex

8. obtuse angle

9. rotation

10. reflex angle

11. rotation angle

12. angle of elevation

13. right angle

14. flat (straight) angle

15. round angle (perigon)

16. null (zero) angle

IV. Give the English equivalents of the following words

and word combinations:

 

тупой угол, развёрнутый угол, нулевой угол, угол возвышения, угол понижения, прямой угол, полный угол, сторона, направление вра­щения, вершина, угол в пределах от 180° 360, вращение (поворот), острый угол, по часовой стрелке, против часовой стрелки, угол враще­ния, направляющий угол.

V. Translate the sentences into English.

1. Если две стороны и угол между ними одного треугольника равны соответственно двум сторонам и углу между ними другого треугольника, то такие треугольники равны.

2. Две прямые называются перпендикулярными, если они пересе­каются под прямым углом.

3. Какой угол называется прилежащим?

4. Докажите, что вертикальные углы равны.

5. Сумма трех этих углов равна 270°.

 

VI. Read the sentences and think of a word which best fits each space.

1. An angle is a... of two lines (the sides or …) meeting at a point called the vertex.

2. Flat (or...) angle means half a... turn.

3. An obtuse angle is greater than an... angle.

4. The measure of a... angle is between 180°and 360°.

5. Angles are classified according to their....

6. Clockwise means the... in which the hands of a clock rotate.

7. The largest angle is the... angle being 360 degrees.

 

VII. Answer the questions on the text "Angles".

1. What is an angle?

2.Can one say that an angle is regarded as the measure of rotation in­volved in moving from one initial axis to coincide with another final axis?

3. What are characteristics of a null angle?

4. An acute angle is an angle between 0° and 90°, isn't it?

5. What are characteristics of an obtuse angle?

6. What are characteristics of a reflex angle?

7. Is there any difference between the angle of depression and the angle
of elevation?

 

TEXT III.

A POLYGON

 

A polygon is a figure formed by three or more points (vertices) joined by line segments (sides). The term is usually used to denote a closed plane fig­ure in which no two sides intersect. In this case the number of sides is equal to the number of interior angles. If all the interior angles are less than or equal to 180°, the figure is a convex polygon; if it has one or more interior angles greater than 180°, it is a concave polygon, A polygon that has all its sides equal is an equilateral polygon; one with all its interior angles equal is an equian­gular polygon. Note that an equilateral polygon need not be equiangular, or vice versa, except in case of an equilateral triangle. A polygon that is both equilateral and equiangular is said to be regular. The exterior angles of a regular polygon are each equal to 360° / n, where n is a number of sides.

The distance from the center of a regular polygon to one of its vertices is called the long radius, which is also a radius of the circumcircle of the poly­gon. The perpendicular distance from the center to one of the sides is called the short radius or apothem, which is also the radius of the inscribed circle of the polygon.

A regular star polygon is a figure formed by joining every m-th point, starting with a given point, of the n points that divide a circle's circumference into n equal parts, where m and n are relatively prime, and n is equal two or greater than 3. This star polygon is denoted by {m/n}. When m = 1, the result­ing figure is a regular polygon. The star polygon {5/2} is the pentagram.