In making horizontal lines, the pupil should make them parallel to the top or bottom of his slate or paper, and in making perpendiculars they should be parallel to the sides of the slate or paper. Parallel lines are lines running in the same direction equally distant from each other in every part; thus, the horizontal lines in figures 1, 2, 3, 4, are parallel to each other. Lines may be drawn parallel at any distance from each other.

13. Draw two parallel horizontal lines, then three, four, five and six.

14. Draw two parallel perpendiculars, then three, four, five and six.

15. Draw an oblique line, and cut it into two, four, three and six parts.

An oblique line is one between a horizontal and a perpendicular; that is, a leaning line..

16. Draw two parallel obliques, then three, four, five and six.

17. Draw parallel lines an inch apart, then half an inch, a quarter, &c.

18. Draw a perpendicular, and cut it into two, three, four, five, six equal parts.

It is difficult to cut a perpendicular into equal parts, because of an optical deception which leads us to think the upper parts shorter than they really are. This errour must be guarded against.

19. Join two dots or points by a right line.

The pupil will move his pencil two or three times from the left dot to the right, before he draws the line. This precaution is more necessary when the operation is performed on paper than when on a slate, where it may be erased if wrong.

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20. Make an acute angle. (fig. 7.)

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Care must be taken to distinguish an angle from what is called its point or apex. The angle is the opening between two lines that meet, and the point or apex is the point where the lines meet. A pair of dividers forms a number of different angles, by being opened more or less.

It is this opening of the sides which determines the size of the angle, and not the length of the sides, which if lengthened out ever so far would not affect the size of the angle.

Imagine two lines which cross each other as in figures 9 and 10. They will make four angles. These are right angles if they are equal, and they will be equal if one line is perpendicular to the line it crosses. If the angle be less than a right angle, it is called an acute angle; if more, it is called an obtuse angle. Acute means sharp, and obtuse means blunt.

21. Make an obtuse angle. (fig. 8.)

22. Make an acute angle with the opening turned upward, downward, to the right and to the left. (Make but one at a time.)

23. Make a triangle. (fig. 11.)

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Close the space between the sides of an angle with a right line, and you make a triangle, a figure which has three angles and three sides.

The base is the side on which the triangle is supposed to rest.

The apex of a triangle is the point opposite to the base. The height of a triangle is a perpendicular drawn from the apex to the base. In the figure it is shown by the dotted line.

A triangle is called Isoceles when two sides are equal. If all three of the sides are equal, it is Equilateral, (which word means equal-sided); and, if all the sides are unequal, it is called Scalene.

24. Raise a perpendicular on a horizontal. (fig.9.) This will produce right angles, as we have before remarked. To ascertain if the angle be exact, take a piece of what is called bonnet paper or thin pasteboard, cut it round, and then cut the round piece into quarters. Each quarter will have two sides at right angles, and by inserting the apex into the opening of the angle drawn by the pupil, any incorrectness will be detected. A small brass or iron square will serve the same purpose, but does not so satisfactorily show that a right angle is equal to a quarter of a circle, which is also called a quadrant.

25. Cross a right line with a perpendicular. (fig.10.) The right line should be drawn in various directions, to show the pupil that a perpendicular may be raised on any right line, whether horizontal or oblique.

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.

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

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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.

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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 two angles are. Figure 14 is what is often called a long or oblong squure.

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

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.

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.