Triangles are made of various substances such as wood, rubber, celluloid, and steel. Wooden triangles are cheap but are likely to warp out of shape; rubber triangles are frequently used, and are, in general, satisfactory; celluloid triangles are extensively used on account of their transparency, which enables the draftsmen to see the work already done even when covered with the triangle.

Fig. 9. 45° and 30° - 60° Triangles.

In using a rubber or celluloid triangle take care that it lies perfectly flat and is hung up when not in use; when allowed to lie on the drawing board with a pencil or an eraser under one corner it will become warped in a short time, especially if the room is hot or the sun happens to strike the triangle.

Triangles from 6 to 8 inches on a side will be found convenient for most work, although there are many cases where a small triangle measuring about 4 inches on a side will be found useful. Every draftsman should have at least two triangles, one having two angles of 45 degrees and one right angle; and the other having angles of 30, 60, and 90 degrees, respectively, Fig. 9.

The value of the triangle depends upon the accuracy of the angles and the straightness of the edges. To test the accuracy of the right angle of a triangle, place the triangle with the lower edge resting on the T-square in position A, Fig. 10. Now draw the line C D, which, if the triangle be true, will be perpendicular to the edge of the T-square. Transfer the triangle to position B, and if the right angle of the triangle is exactly 90 degrees the left-hand edge of the triangle will exactly coincide with the line C D.

Fig. 10. Testing a Right Angle (45° Triangle).

To test the accuracy of the 45-degree angles place the triangle with the lower edge resting on the working edge of the T-square, and draw the line E F, Fig. 11. Now without moving the T-square place the triangle so that the other 45-degree angle is in the position occupied by the first. If the two 45-degree angles coincide they are accurate.

Fig. 11. Testing 45° Angle (45° Triangle).

Triangles are used in drawing lines at right angles to the T-square, Fig. 12, and at an angle with the horizontal, Fig. 13. If it is desired to draw a line through the point P, Fig. 14, parallel to a given line E F, two triangles should be used. First, place triangle A with one edge coinciding with the given line. Now take triangle B and place one of its edges in contact with the bottom edge of triangle A. Holding triangle B firmly with the left hand, slide triangle A to the right or to the left until its edge reaches the point P. The line M N may then be drawn passing through the point P. In place of the triangle B any straight-edge such as a T-square may be used.

Fig. 12. Drawing Vertical Parallel Lines.

Fig. 13. Drawing Parallel Lines at an Angle with the Horizontal.

A line may be drawn through a point, perpendicular to a given line by means of triangles as follows: Let E F, Fig. 15, be the given line, and let the point be D. Place the longest side of triangle A so that it coincides with the line E F. Place the other triangle (or any straight-edge) in the position of the triangle B; then holding B with the left hand, place the triangle A in the position C, so that the longest side passes through the point D. A line may then be drawn through the point D perpendicular to E F.

In previous figures it has been shown how lines may be drawn making angles of 30, 45, 60, and 90 degrees with the horizontal.

Fig. 14. Drawing a Line Parallel to a Given Line.

Fig. 15. Drawing a Line Perpendicular to a Given Line.

It is possible to draw lines forming angles of 15 and 75 degrees by placing the triangles as shown in Fig. 16.

Fig. 16. Drawing Angle of 15° and 75°.

By the use of the triangles and T-square almost any line may be drawn. Suppose it is desired to. draw a rectangle having one side horizontal. First draw by means of the T-square the sides A B and D C horizontal and parallel, Fig. 17. Now place one of the triangles on the T-square and in positions E and F draw the vertical lines D A and B C.

Fig. 17. Drawing a Rectangle with T-Square and Triangle.

If the rectangle is to be drawn in some other position on the board, as shown in Fig. 18, place the 45-degree triangle F so that the longest edge is in the required direction of the side D C. Now, hold the triangle F in position and place another triangle in position H. By holding H in position and sliding triangle F, the sides A B and D C may be drawn. To draw the sides A D and B C change triangle F to position E and repeat the process.