# What is Geometrical construction with example

All QuestionsCategory: Secondary SchoolWhat is Geometrical construction with example

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StopLearn Team Staff answered 1 year ago

Geometrical construction refers to the process of creating geometric figures using only a straightedge (unmarked ruler) and a compass. This technique has been used for centuries in mathematics, engineering, and architecture to accurately and precisely create geometric shapes.
Some common geometrical constructions include:

1. Bisecting a line segment: Given a line segment AB, we can use a compass to draw arcs with centers at A and B that intersect at some point C. Then, we draw a line through C that intersects AB at its midpoint M.
2. Constructing a perpendicular bisector: Given a line segment AB, we can use a compass to draw arcs with centers at A and B that intersect at some points C and D. Then, we draw a line through C and D that intersects AB at its midpoint M. This line is the perpendicular bisector of AB.
3. Constructing an angle bisector: Given an angle ABC, we can use a compass to draw an arc with center at B that intersects the sides of the angle at points D and E. Then, we draw a line through B that intersects DE at its midpoint F. This line is the angle bisector of angle ABC.
4. Constructing a triangle: Given three line segments of lengths a, b, and c, we can use the compass and straightedge to construct a triangle with sides of those lengths. First, we draw a line segment of length a. Then, we draw two circles with centers at the endpoints of the segment and radii of lengths b and c, respectively. The intersection points of these circles give us the other two vertices of the triangle.

These are just a few examples of geometrical constructions. The use of these constructions allows us to create geometric figures with high precision, which is essential in many fields such as engineering, architecture, and art.