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3. The Triangles. — (a) The two triangles commonly used are shown in Fig. 3. One triangle has two angles of 45° each and a right angle; the other has a 30° angle, a 60° angle, and a right angle. The first is called a 45° triangle, the second a 30° or 60° triangle. These triangles are used for ruling straight lines other than horizontal lines, for drawing parallel lines, for erecting a line perpendicular to any other line at any given point, and for drawing lines at certain angles to the horizontal. Various other uses to which the triangles may be put will occur to the draftsman after he becomes accustomed to working with them.

(b) Vertical Lines. — Vertical lines may be drawn with either triangle by placing a short side against the T-square.

(c) Lines Making a Given Angle with the Horizontal. — A 15°, 30°, 45° or n° line is understood to mean a line making an angle of 15°, 30°, 45° or n° respectively with a horizontal line. By placing one edge of the 30° angle of the triangle against the T-square a 30° line can be drawn in four directions from any given point. By using the other angles, 45° and 60° lines can likewise be drawn. By combining the two triangles 15° and 75° lines can be drawn. Thus by means of the T-square and triangles a circle can be divided into twenty-four equal segments by drawing from its centre 15°, 30°, 45°, 60°, and 75° lines in each of the quadrants formed by a horizontal and a vertical line intersecting at the centre of the circle.

(d) To Draw One or More Lines Parallel to a Given Line. — Make any edge of one of the triangles coincide with the given line and bring an edge of a second triangle into perfect contact with one of the two remaining edges of the first triangle. Hold the second triangle perfectly stationary and slide the first triangle upon it. Either triangle may be used for the first one, a little practice enabling one to choose the most convenient arrangement for any given case.

(e) To Erect a Perpendicular to any Line at any Given Point. — Make one edge of the right angle of either triangle to coincide with the given line. Bring an edge of a second triangle into perfect contact with the hypotenuse edge of the first triangle. Slide the first triangle upon the second.

(f) Second Method. — Make the hypotenuse edge of either triangle coincide with the given line. Bring an edge (preferably the longest edge) of a second triangle into contact with one of the two remaining edges of the first triangle. Holding the second triangle stationary, turn the first triangle to the position shown in Fig. 1. This method can often be used where the first method cannot.

(g) In all of the three methods here given, the greatest care should be exercised to prevent the stationary edge from slipping; the second triangle being held firmly in place with the left hand until the first triangle has been moved to the desired position ; the left hand can then hold both triangles, leaving the right band free to use the pencil. If only one line is to be drawn, it is evident that when the first triangle has been moved to its final position the second triangle need no longer be held in place. In large drawings it will often be found of advantage to use the T-square in place of the stationary triangle.

(b) Vertical Lines. — Vertical lines may be drawn with either triangle by placing a short side against the T-square.

(c) Lines Making a Given Angle with the Horizontal. — A 15°, 30°, 45° or n° line is understood to mean a line making an angle of 15°, 30°, 45° or n° respectively with a horizontal line. By placing one edge of the 30° angle of the triangle against the T-square a 30° line can be drawn in four directions from any given point. By using the other angles, 45° and 60° lines can likewise be drawn. By combining the two triangles 15° and 75° lines can be drawn. Thus by means of the T-square and triangles a circle can be divided into twenty-four equal segments by drawing from its centre 15°, 30°, 45°, 60°, and 75° lines in each of the quadrants formed by a horizontal and a vertical line intersecting at the centre of the circle.

(d) To Draw One or More Lines Parallel to a Given Line. — Make any edge of one of the triangles coincide with the given line and bring an edge of a second triangle into perfect contact with one of the two remaining edges of the first triangle. Hold the second triangle perfectly stationary and slide the first triangle upon it. Either triangle may be used for the first one, a little practice enabling one to choose the most convenient arrangement for any given case.

(e) To Erect a Perpendicular to any Line at any Given Point. — Make one edge of the right angle of either triangle to coincide with the given line. Bring an edge of a second triangle into perfect contact with the hypotenuse edge of the first triangle. Slide the first triangle upon the second.

(f) Second Method. — Make the hypotenuse edge of either triangle coincide with the given line. Bring an edge (preferably the longest edge) of a second triangle into contact with one of the two remaining edges of the first triangle. Holding the second triangle stationary, turn the first triangle to the position shown in Fig. 1. This method can often be used where the first method cannot.

(g) In all of the three methods here given, the greatest care should be exercised to prevent the stationary edge from slipping; the second triangle being held firmly in place with the left hand until the first triangle has been moved to the desired position ; the left hand can then hold both triangles, leaving the right band free to use the pencil. If only one line is to be drawn, it is evident that when the first triangle has been moved to its final position the second triangle need no longer be held in place. In large drawings it will often be found of advantage to use the T-square in place of the stationary triangle.

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