Constructions

To draw accurate figure some basic geometrical instruments are needed such as a graduated scale, a pair of set-squares, a pair of dividers with adjustments, a pair of compasses with provision of fitting a pencil at one end and a protractor.

A geometrical construction is the process of drawing a geometrical figure using only two instruments – an ungraduated ruler, and a compass. A graduated scale and a protractor are used in construction where measurements are also required.

Following are some basic constructions: a) To bisect a given angle. b) To draw the perpendicular bisector of a given line segment. c) To construct an angle of 30°, 45°, 60° etc. Construction of a triangle is unique if: (i) two sides and the included angle are given, (ii) three sides are given, (iii) two angles and the included side are given and, (iv) in a right-angled triangle, hypotenuse and one side are given. At least measurements of three parts of a triangle are required for constructing it but not all combinations of three parts are sufficient for the purpose. A unique triangle can also be constructed if its (i) base, a base angle and the sum of the other two sides are given, (ii) base, a base angle and the difference of the other two sides are given, (iii) perimeter and its two base angles are given.

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