Εικόνες σελίδας
PDF
Ηλεκτρ. έκδοση

26. Draw a rectangular, or right angled triangle, (figs. 12 and 13.)

This is a triangle of which one of the angles is a right angle, as the lower left hand one in fig. 12, and the top one in fig. 13. The base may be horizontal or inclined.

27. Make a rectangular isoceles triangle.

There is no difference between this and figures 12 and 13, except that in an isoceles triangle, two of the sides must be of equal length. In fact, fig. 12 is an isoceles.

Figure 13, though rectangular, is a scalene also.

(12)

28. Draw a rectangle. (fig. 14.)

(13)

A rectangle is properly a figure with four sides, of which each two opposite sides are equal and parallel, and of which all the angles are right angles.

[merged small][ocr errors][merged small]

The lower side is the base, and the right or left side is the height.

To ascertain its correctness, the Monitor may examine every angle with his quadrant of pasteboard, or he may with his dividers see if the left hand upper, and

right hand lower angles are as far apart as the other Figure 14 is what is often called a

two angles are.

long or oblong square.

29. Make a rectangle, and cut it into equal right angles. (fig. 15.)

(16)

(17)

30. Make a parallelogram, and mark its height. (fig. 16.)

The parallelogram, like the rectangle, has its opposite sides parallel, but none of its angles are right. The height is a perpendicular dropped from the top to the base, and is marked by the dotted line in the figure.

31. Make a square. (fig. 17.)

This figure has its four sides equal, and all its angles right.

(18)

(19)

32. Draw two angles with parallel sides. (figs. 18 and 19.)

Two angles, as in fig. 18, are called parallel, not because their sides are of equal length, but because their openings and points correspond exactly. Fig. 19 is designed to exercise the pupil in making parallel angles in various positions.

1/4

33. Draw obliques equidistant (that is, equally distant) from a perpendicular..

Draw first a horizontal, raise a perpendicular on its centre, and then draw a line from the top of the perpendicular to each end of the horizontal. The figure will then be an isoceles triangle, as in fig. 11.

34. Make a scalene triangle. (fig. 13.)

As it is not difficult to make a triangle of unequal sides, it will be well for the monitor to prescribe the length of one or more of them. Thus, he may say: "Make a scalene triangle, of which the three sides shall measure inches, one inch, and a half inch."

[ocr errors]

35. Make an equilateral triangle. (fig. 20.)

After the pupil makes the figure exactly, let the length of the sides be given, as one, two, three, &c. inches. Then require the point to be under the base, turned to the right, &c.

36. From a given point draw a perpendicular.

First draw a right line, then make the proposed point, and lastly draw the perpendicular.

37. Raise a perpendicular on the end of a right line. (22)

(20)

(21)

38. Make a Rhomb or Lozenge. (fig. 21.)

The four sides are equal as in the square, but the angles are not right angles. To draw this figure, make a right line, cross it with a perpendicular, like the dotted lines in the figure, and then draw the sides.

If the Rhomb or Lozenge have all the angles equal, the figure is merely a square placed obliquely, as in fig. 22.

(23)

(24)

39. Cut a rectangle into halves. (fig. 23.)

This will make two angles, whose exactness may be tested by an eighth part of a circle of pasteboard, the rectangle being quarter of a circle, as was stated under Prop. 24.

40. Cut an acute angle into two equal parts. (fig.24) 41. Double an angle.

then make another Suppose the lower then by making the

Make an angle of any size, and of the same size by the side of it. angle of fig. 24 to be made first, upper right line, the angle will be doubled.

(25)

42. Triple an angle. (fig. 25.)

(26)

43. Cut an angle into three equal parts. (fig. 25.) 44. Cut an angle into six equal parts. (fig. 26.) These three propositions need no explanation.

trapezoid

when bases are

(1)

SECOND CLASS.

(2)

1. Make two angles of perpendicular sides.

After having made one angle, the pupil will draw a perpendicular to one of the sides, and then a perpendicular to the other side, until the perpendiculars cross

each other.

One of the angles is acute, and the other obtuse; and if you lengthen one of the perpendiculars, a new angle will be formed exactly like the angle first made, as the dotted continuation of the perpendicular in fig. 1 shows.

2. Make two triangles of perpendicular sides. (fig.2.) Make one triangle, and then draw a perpendicular to each side, until the perpendiculars touch and form angles. Each side of each triangle must be perpendicular to some side of the other triangle.

(3)

3. Make a trapezium. (fig. 3.)

A Trapezium has four sides, of which, two, called the bases, are parallel. In the figure, these are the upper and lower sides. The height is a perpendicular from base to base. As this figure is easily made, the length of the bases and the height may be given: thus, "Make a trapezium whose, height shall be one inch, and whose bases shall be an inch and a half, and two inches.'

« ΠροηγούμενηΣυνέχεια »