Mastering basic geometrical constructions is a core skill in graphical communication and technical drawing. These constructions—such as bisection of a line, division of a line, angle bisectors, and constructing perpendiculars are the foundation for understanding more advanced topics in geometry, engineering, and design.
Using only a compass, straightedge, and pencil, students learn to solve spatial problems with logic, precision, and confidence. These timeless techniques, often used in exams like the SEC Graphical Communication paper, are essential for creating clean, accurate technical drawings by hand. They also build visual literacy and problem-solving skills that are valuable in subjects like mathematics, physics, and engineering drawing.
This guide provides a step-by-step explanation for each type of construction, complete with diagrams and tips. If you are a secondary school student preparing for exams this page will help reinforce the principles of geometrical construction in an accessible and practical way.
Geometrical constructions are visual methods of solving mathematical problems using tools such as a compass, ruler, and protractor. Unlike numerical methods, constructions focus on accuracy through drawing, making them essential in fields such as architecture, design, and engineering. This section covers four critical types of constructions: bisection of a line, division of a line into equal parts, bisection of an angle, and construction of perpendicular lines.
Bisection of a line involves dividing a straight segment into two equal parts. This is one of the simplest and most frequently used techniques in geometry. It lays the groundwork for symmetry and midpoints, concepts used in both construction and real-world applications such as design layouts and machine parts.
Division of a line into equal segments is especially useful when spacing components or creating repeated elements in a design. This technique requires careful angle construction and the use of parallel lines, helping students develop their understanding of ratio and proportion in a geometric context.
Bisecting an angle teaches students how to split any given angle into two identical halves using only a compass and straightedge. This skill is essential for creating accurate joints, corners, and symmetrical shapes in technical drawing.
Constructing perpendiculars is crucial for achieving right angles in technical diagrams and working drawings. Perpendicular lines appear frequently in orthographic projection, architectural layouts, and CAD designs. Students will learn how to construct perpendiculars both from a point on a line and from a point outside a line.
All constructions in this guide are explained step-by-step with supporting illustrations, making them easy to follow for beginners. Students can use these methods to solve exam problems, reinforce classroom learning, and build a deeper understanding of geometric principles.
By practising these basic geometrical constructions regularly, learners develop precision, spatial awareness, and the confidence needed for more advanced graphical communication tasks. These skills serve as the foundation for topics such as orthographic projection, isometric drawing, and solid geometry. Mastering them is the first step toward becoming fluent in the universal language of technical drawing.
