Constructions

11.1 Introduction

We have learnt about the many shapes and diagrams, which were necessary to prove a theorem or solving exercises.

Normally, all these instruments are needed in drawing a geometrical figure, such as a triangle, a circle, a quadrilateral, a polygon, etc. with given measurements. But a geometrical construction is the process of drawing a geometrical figure using only two instruments — an ungraduated ruler, also called a straight edge and a compass. In construction where measurements are also required, you may use a graduated scale and protractor also.

11.2 Basic Constructions

Here you will have learnt how to construct a circle, the perpendicular bisector of a line segment, angles of 30°, 45°, 60°, 90° and 120°, and the bisector of a given angle, without giving any justification for these constructions.

Construction 11.1 : To construct the bisector of a given angle.

Construction 11.2 : To construct the perpendicular bisector of a given line segment.

Construction 11.3 : To construct an angle of 60° at the initial point of a given ray.

11.3 Some Constructions of Triangles

As some constructions of triangles will be done by using the constructions given in earlier classes. You may have noted that at least three parts of a triangle have to be given for constructing it but not all combinations of three parts are sufficient for the purpose.

Construction 11.4 : To construct a triangle, given its base, a base angle and sum of other two sides.

Construction 11.5 : To construct a triangle given its base, a base angle and the difference of the other two sides.

Construction 11.6 : To construct a triangle, given its perimeter and its two base angles.