Theory

Geometrical construction is one of the main parts of engineering drawing which involves drawing shapes and figures with the help of a ruler and a compass. Geometrical construction is mainly based upon the plane geometry. It consists of drawing and bisecting lines, creating angles, constructing different types of polygons etc. In fields like engineering and architecture, constructions ensure precise representation of shapes, angles, and dimensions. This accuracy is essential for creating functional and structurally sound designs. Geometrical constructions assist in establishing symmetry and centrelines, guiding the positioning of features and ensuring balance in designs.

Geometrical construction mainly consists the following problems:

• Bisecting a line: Dividing a line segment into two equal parts by drawing a perpendicular bisector through its midpoint.

• Drawing perpendiculars: Creating lines that intersect at right angles to a given line or at the midpoint of another line.

• Drawing parallel lines: Constructing lines that maintain an equal distance from each other and never intersect.

• Dividing a line into equal parts: Subdividing a line segment into a specified number of equal segments.

• Dividing a circle: Splitting a circle into equal or specified fractional parts using geometrical methods.

• Bisecting an angle: Dividing an angle into two equal angles by constructing its angle bisector.

• Trisecting an angle: Dividing an angle into three equal parts using geometric methods.

• Finding the center of an arc: Locating the midpoint or center point of an arc using geometrical methods.

• Constructing an ogee or reverse curve: Drawing a smooth, S-shaped curve with specific proportions and characteristics.

• Constructing equilateral triangles: Creating triangles with all sides of equal length and all angles measuring 60 degrees.

• Constructing squares: Drawing quadrilaterals with all sides equal in length and all angles measuring 90 degrees.

• Constructing regular polygons: Creating polygons with equal side lengths and equal interior angles using geometric methods.

• Special methods of drawing: Various techniques for creating specific shapes or patterns using geometric methods.

• Regular polygons inscribed in circles: Drawing polygons whose vertices lie on the circumference of a circle.

• Drawing regular figures using T-square and set-squares: Constructing shapes using tools like T-squares and set-squares to ensure accuracy.

• Drawing tangents: Creating lines that touch a curve at a single point, without intersecting it.

• Lengths of arcs: Determining the measure of the arc length along a circle using geometric methods.

• Circles and lines in contact: Drawing circles and lines that are tangent to each other at their point of contact.

• Inscribed circles: Constructing circles that fit snugly inside polygons, touching each side at a single point.