Next to the T-square the two triangles shown in Figure 2 are your most useful drawing board tools. All lines that you draw, with the exception of horizontal lines, are to be drawn with these triangles. Never use a ruler or a scale to draw lines—use the triangles.

Both the triangles shown are right triangles-one angle in each is a right angle, or 90 degrees. The triangle shown in Figure 2a is called a 30-60 because its other two angles are 30 and 60 degrees respectively, while the triangle shown in 2b is called a 45 because both of its other angles are 45 degrees. Either triangle may be used to draw vertical lines, while the 30-60 triangle is used to draw lines at angles of 30 and 60 degrees, and the 45 triangle is used to draw angles of 45 degrees. By adding or subtracting the two triangles we can draw an angle of 75 (30+45), or an angle of 15 (45—30); we are therefore able to draw angles at 15 degree intervals; viz: 15, 30, 45, 60, 75 and 90.

Now follow these steps carefully and do everything that you are told to do:

FIRST:

Take either triangle and place it against the T-square as shown in the drawing B, holding both T-square and triangle firm with the left hand. Now draw a vertical line, beginning at the bottom of the triangle and moving up toward the apex. Now slide the triangle to the right a little and draw another vertical line in the same way. Do this again and again until you have drawn at least ten vertical lines.

SECOND:

Now draw a sloping line along the hypotenuse of the triangle by going from the apex to the base, as shown in Figure 3a. If the 30-60 triangle is in the position shown, this line will make an angle of 60 degrees with the horizontal on one side and 120 degrees on the other side. If the triangle is in the position shown in 3c, the line will make an angle of 30 degrees with the horizontal on one side and 150 degrees on the other.

THIRD:

Now move the triangle far over to the right, as shown in Figure 3b. In this position, the triangle is not convenient for drawing a vertical line, so you will have to reverse it, as shown in that figure. You will also have to reverse the direction of the line, this time going from apex to base, as indicated by the arrow. Remember this simple rule: lines go up on the left and down on the right·           

FOURTH:

By keeping the triangle in the position shown in 3b and sliding it along the T-square to the left, drawing lines along the hypotenuse each time you get into a new position, you will have a series of parallel lines all 60 degrees with the horizontal. In a similar way, if you hold the triangle in the position shown in 3c, sliding it along the T-square to the right and drawing lines along the hypotenuse each time you get to a new position, you will have a series of parallel lines all 30 degrees to the horizontal. If you did the same thing with the 45 triangle, your parallel lines would all be 45 degrees with the horizontal.

FIFTH:

Practice drawing right angles as follows: draw a line with the 30-60 triangle at 60 degrees to the horizontal; then turn it around to draw another line at 30 degrees to the horizontal. These two lines will cross at right angles. Try this several times to make sure you know how to draw a right angle by means of the 30-60 triangle, without using the right-angle part of the triangle. Try it with the 45 triangle.

SIXTH:

Hold one triangle still and slide the other triangle along it as shown in Drawing C and also in Figure 4. This will enable you to draw parallel lines at any angle at all. You merely use the edge of one triangle as you used the edge of the T-square. This is also shown in the picture.

If you want to draw any line at any angle, use the edge of one of the triangles. Remember, the scale and the ruler should be used for measuring only, and not for drawing lines. By means of the two triangles and T-square, you can draw lines horizontally and vertically, at 15, 30, 45, 60, 75 and 90 degrees. You can also get angles of 105, 120, 135, 150, 165 and 180 degrees by the same method of adding and subtracting the 30 and 45.

Practice drawing lines at angles with these two triangles against your T-square. Draw as many as you can in order to "get the feeling." Then, in pencil, try to draw the figures given on the next page in Lesson 3.

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