Measuring and constructing angles with a protractor

Angles of any given size may be drawn, or the size of any angle may be measured, by using an instrument called a pro­tractor (Fig. 13).

A protractor is a semicircular plate graduated from one extremity of the diameter to the other and used to measure angles. The inside numbers show angles in degrees beginning at 0° and going counterclockwise. The outside numbers mark angles in degrees from 0° going clockwise.

Notice that the upper part of the protractor is half a circle. It contains 180 parts. The centre of the semicircle or protractor ,is at point 0. Notice that there are two sets of

Fig. 13 Fig. 14

numbers on the curved edge so arranged that one set of numbers begins at the right side of the Protractor and the other begins at the left side. This arrangement permits us to measure angles that open at the left or the right sides.

Problem: Find the number of degrees in angle EFG (Fig. 14) Method: Place the centre of the protractor at point F so the Point 0 of the protractor is on point F and the zero division line at S on the protractor lies on side FG of the angle. Now read the scale where lines Fe crosses the protractor. Reading from the zero at the right we find that angle EFG contains 30°.

If you were to use¹ the outside scale which starts at zero on the left side of the protractor, the reading would be 150°. Since a 150° - angle would be obtuse, and EFG is acute, you would not have the correct measurement for the angle.

Note:

¹ if you were to use — если бы вы использовали

Exercises

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

inside, size, side, acute, obtuse, measuring, constructing, arranging, angle, edge, arrange, circle, semicircle.

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

if you were to use, is used to measure, may be drawn, protractor, counterclockwise, permits us to measure, to calculate.

III. Answer the following questions:

1 What is a protractor used for? 2. What do inside numbers on the scale of a protractor show? 3. How many parts does the upper part of the protractor contain? 4. What permits us to measure angles that open at the left or at the right side?

4. Translate into English:

Для измерения углов употребляется специальный прибор- транспортир. Этот прибор представляет собой полукруг, дуга которого разделена на 180 частей. Чтобы измерить угол, накладывают транспортир так, чтобы Центр транспортира совпал с вершиной угла, а радиус был расположен на одной стороне угла. Тогда число градусов, содержащихся Луге заключенной между сторонами угла, покажет нужную величину. При помощи транспортира можно также начертить угол, содержащий данное число градусов.

TEXT

Kinds of polygons

Triangles. A triangle is a plane figure bounded by three straight lines and containing three angles. The sum of the angles of every triangle is 180°.

A triangle is identified by naming its vertices in any order. Thus, the triangle given in the figure 15 may be called ∆АВС, ∆BAC, ∆ВСA, ∆САВ, ∆CBA or ∆AСВ. The symbol ∆ means triangle.

Fig. 16 shows the various types of triangles. A scalene triangle (Fig. 15) is a triangle with no two sides equal. An isosceles triangle is a triangle which has two equal sides. The equal sides are called the legs; the third side is called the base. The angles at the base are called the base angles. The angle formed by the two equal sides, is called the vertex angle. An equilateral triangle is a triangle with all three sides equal.

Quadrilaterals. A quadrilateral is a plane figure bounded by four straight lines. There are several kinds of quadrilat­erals (Fig. 17).

A parallelogram is any quadrilateral in which two pairs of opposite sides are parallel.

A rectangle is a parallelogram whose angles are all right angles.

A square is a rectangle in which all the sides are equal in length.

A trapezoid is a quadrilateral in which only one pair of opposite sides are parallel.

The rectangle and the square both have four right angles. You have learned how to draw a 90º-angle with a protractor and construct the angle with" compasses. Using this knowl­edge, you can construct rectangles and squares.

Other Plane Figures (Fig. 18). A pentagon is a polygon which has five sides. A hexagon is a polygon which has six sides. An octagon is a polygon which has eight sides. A deca­gon is a polygon, which has six sides.

Since a regular polygon has equal sides and equal angles, all the vertices are equidistant from the centre.

A circle is a curved line a11 points of which are equidistant from the centre. Therefore, If we inscribe a regular polygon inside of a circle every vertex of the polygon will rest on the line of the circle.

Perimeter. The perimeter of a plane figure is the line around it. The perimeter of each the figures we have been studying would equal the sum of the lengths of its sides.

The perimeter of g rectangle equals two times the length plus two times the width

p = 2l + 2w or p = 2(l + w).

Since a square is a rectangle having four equal sides, we can represent each of the sides by the letter s. The perimeter of the square is expressed by the formula

p = s + s + s + s,

which is written as: p=4s.

The perimeter of a square equals the length of one side mul­tiplied by 4.