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I share this viewpoint You are wrong there, I am afraid
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1. In a plane all the points at a given distance from a given fixed point are said to form a chord.
2. The diameter passing through the circle centre, is the shortest chord in a circle.
3. Angle POQ is called a central angle because its vertex is at the centre of the circle.
4. A tangent to a circle is a curved line that touches the circle at two points.
5. A secant is an extended chord: a straight line cutting the circle at a single point.
6. Mathematicians have discovered that the ratio of the circumference to a diameter is the same for all circles.
7. The circumference of a circle may be defined as the limit of the perimeter of an circumscribed regular polygon.
8. The equation x2 + y2 = r2 is the equation of the semicircle.
Ex.8. Fill in the blanks with necessary words and word combinations. Mind there are two extra words.
| a. a line segment; b. only; c. circumscribed; d. vertex; e. circumference; f. through; g. in a plane; | h. are said; i. bisect; j. arc; k. a chord; l. given; m. on the circle; n. intersect; | o. a set of points; p. fixed; q. meaning; r. the measure; s. connects; t. perimeter |
1. A circle is... in a plane, all of which are the same distance from a... point.
2. A radius is... from the center of a circle to a point....
3. Tangent circles are two circles that...... at one point.
4. A... circle is a circle passing... each... of a polygon.
5.... all the points of a given distance from a given... point... to form a circle.
6. The word... comes from a Latin word... “bow”.
7. A diameter is... which... the center to any points on the circle.
8. We cannot find... of a circle by adding... of the segments.
Ex.9. Match the definitions of the circles with their names.
Based upon their relative positions, two circles in a plane or a circle and a polygon have special names.
| 1. Tangent circles 2. Concentric circles 3. A circumscribed circle 4. Externally tangent circles 5. An inscribed circle 6. Eccentric circles 7. Inscribed polygon 8. A circumscribed polygon 9. Internally tangent circles | a. are circles that have different centers. b. are both circles which are on the opposite sides of the tangent line. c. is a polygon that is inside a circle so that each of its vertices lies on the circle. d. is a circle to which all the sides of a polygon are tangents. e. is a polygon that is outside the circle in such a way that all of its sides are tangent to the circle. f. is a circle passing through each vertex of a polygon. g. both circles which are on the same side of the tangent line. h. are two or more circles in a plane with the same center, but the lengths of their radii vary. The annulus is the region between concentric circles. i. are two circles that intersect only at one point. |
Ex.10. Let us revise the Degrees of Comparison. Give the best English equivalents for the words in parentheses.
1. A circle is (самая простая) of all curved lines.
2. Every point at a distance (больше) than radius (говорят) to be outside the circle.
3. A secant segment is a line segment with an endpoint in the exterior of a circle, and the other endpoint on the circle, (самой далекой) from the external point.
4. Tom comes top in all the exams – he must be (самый умный) student in the group.
5. (Чем меньше) students think, (тем больше) they talk.
6. How are you today? – I’m very (хорошо), thanks.
7. Is this proof (более правильно)?
8. Peter speaks English (наиболее бегло) of all the students in this group.
9. (Чем больше) I learn, (тем больше) I forget and (тем меньше) I know.
10. (Чем скорее) the problem is solved, (тем лучше).
11. This contribution of the ancient Greeks is (намного больше, чем) the formulas of the Egyptians.
Ex. 11. Translate into Russian, paying attention to the degrees of comparison.
1. The diameter is the longest possible chord of any circle.
2. The lecture given to the second-year students last week was not as complicated as the one the professor delivered last month.
3. The science advisor was very glad that his postgraduates continued further discussion.
4. The maths lessons are getting more and more difficult in the third year of studies.
5. For the 8.15 class, the latest the students must leave the hostel is 7.40.
6. The diameter is twice as long as the radius.
7. A major arc is an arc greater than a semicircle but less than 3600.
8. His argument is less convincing than his proof.
9. The ruler is the simplest instrument for drawing.
10. The proof is not so valid as he supposed at first.
Ex. 12. Choose the correct variant.
1. These rules are... to understand than others.
a) so difficult b) more difficult c) much difficult
2. We have never been... than on that day.
a) more happier b) the happiest c) happier
3. This is... translation I have ever done.
a) the most worse b) the worst c) the worser
4. Can you repeat... sentence.
a) the latest b) the least c) the last
5. Which is... textbook of the two?
a) better b) the best c) the better
6. I don’t think this is... thing for us at the moment.
a) a more important b) much more important c) the most important
7. She is getting... with every day.
a) more weaker b) the weakest c) much weaker
8. Girls tend to be... than boys.
a) more tidier b) tidier c) much tidy
9.... than twenty students passed all the exams.
a) a fewer b) a few c) fewer
Ex. 13. Ask special questions using the words in parenthesis.
1. An arc is usually named by its endpoints. (how)
2. A chord is a line segment connecting any two points on the circle. (what)
3. They attended the lectures on geometry twice a week. (how often)
4. Most mathematical proofs can be given in many different ways. (how)
5. In geometry we separate all geometric figures into two groups: plane figures and space figures or solids. (how many)
6. Later you ought to do some measurements to check your calculations. (when)
7. We are already familiar with the basic concepts of geometry through our high school studies of maths. (what)
8. The points of geometry have no size and no dimensions. (what)
9. Numbers became abstract when we began to reason about their nature and enumerate their properties through arithmetical and logical operations. (when)
10. A straight line extends indefinitely only in one direction. (where)
11. Every math problem must be settled either in the form of a direct answer to the question, or by the proof of the impossibility of its solution. (how)
12. The Greeks were able to carry out many constructions with two tools. (how many)
13. The theory in question was developed successively by different scientists. (who)
Ex. 14. Choose the correct variant of translation.
Дата публикования: 2015-02-28; Прочитано: 285 | Нарушение авторского права страницы | Мы поможем в написании вашей работы!
