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Post-Reading Activity. Ex. 4. Answer the following questions
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Ex. 4. Answer the following questions.
1. What is a principal way to discover properties of geometries figures?
2. Dwell on the types of propositions.
3. What is a definition?
4. Axioms are statements that must be proved, aren’t they?
5. What is particular about theorems?
6. Does a corollary follow directly from a definition or from a theorem?
7. How many parts can one distinguish in any theorem?
8. Can the hypothesis of one theorem become the conclusion of the other?
9. Give your own examples of two theorems which are converse to each other.
10. What is the difference between an assumption and an axiom?
Ex. 5. Match the English words and word combinations with their Russian equivalents.
| 1. the process of reasoning 2. to discover properties of figures 3. what meaning one attributes 4. to accept without proof 5. there is a unique line 6. to lie in the same plane 7. congruent arcs 8. the remaining angles 9. to intersect at one point 10. under this hypothesis 11. to be converse to the given theorem 12. to begin with the words 13. to draw a bisector | a. пересекаться в одной точке b. существует единственная линия c. какое значение придают d. процесс рассуждения e. начинать со слов f. конгруэнтные дуги g. обнаружить свойства фигур h. принимать без доказательства i. остающиеся углы j. провести биссектрису k. быть обратным данной теореме l. по этой гипотезе m. лежать на одной плоскости |
Ex. 6. Find out whether the statements are True or False according to the information in the text. Use the introductory phrases:
| I think, it is right. Quite so. Absolutely correct. I quite agree to it. | I am afraid, it is wrong. I don’t quite agree to it. On the contrary. Far from it. |
1. In geometry all facts are expressed in the form of formulas.
2. Two parts are distinguished in any theorem: the proposition and the conclusion.
3. Scientists discover properties of geometric figures by means of reasoning.
4. Corollaries follow directly from definitions.
5. We obtain a converse theorem by replacing the hypothesis of the given theorem with the conclusion.
6. The direct and the converse theorems always turn out to be true.
7. Axioms are postulates which should be proved.
8. There are two types of propositions: congruent and central.
9. In any theorem the hypothesis can begin with the word “if”, and the conclusion with the word “then”.
Ex. 7. Fill in the blanks with the words from the box. Mind there are two extra words.
| a. hypothesis b. further c. theorems d. reasoning | e. accepted f. meaning g. to discover h. conclusion | i. deduced j. remaining k. established l. propositions |
1. All that is necessary is that the words and phrases used shall have the same... for everybody.
2. The... that we take for granted without proof are called assumptions.
3. That which is given is sometimes called the..., and that which is to be proved is sometimes called the....
4. Propositions that can be logically deduced from the assumptions are often called....
5. All facts... in geometry are expressed in the form of propositions.
6. The answer to a problem in actual life can often be obtained by... investigation of the actual facts, while in geometry it can always be obtained by... alone.
7. The scientist has two problems – one,... new scientific propositions; the other, to devise a set of assumptions from which all his propositions can be logically....
Ex. 8. Match the left and the right parts of the following statements.
| 1. If the same quantity is added or subtracted from equal quantities, then 2. If two points of a line lie in a given plane, then 3. If each of two quantities is equal to a third quantity, then 4. If central angles are congruent, then 5. If a number is divisible by 2 and by 3, then 6. If one of the four angles formed by two intersecting lines is right, then | a. these two quantities are equal to each other. b. it is divisible by 6. c. the equality remains true. d. the remaining three angles are right as well. e. all points of this line lie in the same plane. f. the corresponding arcs are congruent. |
Ex. 9. Translate the sentences according to the models.
Model 1. There are various ways of evaluating formulae.
Существуют различные способы вычисления формул.
1. There are a lot of important theorems in this book.
2. There are sets containing no elements.
3. There has been recently developed a new method of proving the theorem.
4. There are many measurements to be made.
5. There weren’t any problems with my term paper last year.
6. There will be enough work for everybody at the next conference.
Model 2. There exist a lot of equivalent relations.
Существует много эквивалентных отношений.
1. There exists no difference between these two expressions.
2. There exists at least one element in a non-empty set.
3. There exist some important statements in the article.
4. There exist many different ways of defining a circle.
5. There exist no solutions to the problem presented.
Model 3. To a pair of numbers there corresponds a point in the plane.
Паре чисел соответствует точка на плоскости.
1. To a linear equation there corresponds a straight line in the Euclidean space.
2. To a point in three dimensional space there correspond its three coordinates.
3. To each number in X there corresponds a unique element in Y.
4. To any two objects a, b there corresponds a new object.
5. If to each member x of a set there corresponds one value of a variable y, then y is a function of x.
Ex. 10. Let us revise Present, Past and Future Simple Tenses (Active and Passive).
Дата публикования: 2015-02-28; Прочитано: 623 | Нарушение авторского права страницы | Мы поможем в написании вашей работы!
