Exercises

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

vertices, isosceles, inscribe, describe, equal, curve, square, rectangle, quadrilaterals, right, parallel, trapezoid, hexagon, octagon, decagon.

2. Underline the prefixes and state their meanings:

polygons, hemisphere, transport, triangle, extraordinary, discharge, semicircle, equilateral, subway, international, coexistence, unequal.

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

two times the, length, two times the width, bounded by, to inscribe, equidistant.

4. Answer the following questions:

1. What is a polygon? 2. What triangles do you know? 3. What kind of quadrilaterals do you know? 4. What is a plane figure? 5. What is the perimeter of a plane figure?

5. Translate into Russian:

The name of the triangle is derived from the Latin word "triangulum"=three-angle, which in its turn was derived from the Greek word "tri-gonon" or three-angle.

Cut a square of convenient size from a sheet of paper. Make a fold from one corner to the opposite corner. Into what kind of triangles is the square divided by the fold in the pa­per?

6. Translate into English:

Треугольник — это плоская фигура, ограниченная тре­мя линиями и содержащая три угла.

Треугольники бывают равносторонние, разносторон­ние, равнобедренные.

Четырехугольники — это тоже плоские фигуры. Если стороны четырехугольника равны и все углы прямые, то такой четырехугольник называется квадратом.

Многоугольники — это также плоские фигуры. Пяти­угольник имеет пять сторон, шестиугольник — шесть, восьмиугольник — восемь, десятиугольник — десять сто­рон.

Линия вокруг плоской фигуры называется перимет­ром. Периметр плоской фигуры равен сумме длин его сто­рон.

TEXT

Circles

A circle is a plane figure bounded by the curved line all points of which are the same distance away from the fixed point, called the centre. The length of the curved line, or the distance around the circle, is its-circumference. A straight line drawn from the centre to any point on the circumference is called a radius (plural: radii). OD the radios (see Fig. 19). The straight line that passes through the centre of the circle and both of whose ends are on the circumference is called a diameter. AB is the diameter. A line segment that connects any two points on the circumference of a circle is a chord. An example is BC.

A ny part of curved line which makes the circle is an arc. The portion of the circle confined in AOD is a sector of the circle, for two sides are radii and the third side is an arc. Because its vertex is at the centre, angle AOD is a central angle.

When a circle is cut in half, each of the halves is called a semi­circle. When a circle is cut into four equal parts, each of the quarters is called a quadrant.

Area of a Circle. If a circle is divided into 4 quadrants and a square is circumscribed about the circle, four small squares are formed (Fig. 20). The side of each small square equal to the radius r. The area of each small square is r²; the area of the large square is equal to the sum of the four small squares, or 4r².

We can see that the area of the circle is about ¾ of the large square. It is approximately equal to 3 ¹/₇ of the small squares, or 3 ¹/₇ r². This can be also written πr².

Rule to remember: the area of a circle equals π, times the radius squared

A= πr².