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.