# Practical Geometry

## The following mathematical instruments are used to construct shapes: A graduated ruler: A ruler ideally has no marking on it. A ruler is used to draw line segments and to measure their lengths. The pair of compasses: A pair of compasses is used to mark off equal lengths but not to measure them and to draw arcs and circles pair of compasses is used. Divider: The divider has a pair of pointers. A divider is used to compare the lengths. Set squares: Two triangular piece, one of them has 45°, 45°, 90° angles at the vertices and the other has 30°, 60°, 90° angles at the vertices. Set squares are used to draw perpendicular and parallel lines. Protractor: A semi-circular device graduated into 180° where the measure starts from 0° on the right hand side and ends with 180° on the left hand side and vice-versa. A protractor is used to draw and measure angles. A circle is a shape with all the points are at the same distance from its center. Using the ruler and pair of compasses, a circle can be constructed when the length of its radius is known. A part of line that has two end points and has a definite length is called a line segment. A line segment can be drawn if its length is given. A line segment having length equal to a given line segment can be drawn using ruler and compass. A line which cuts another line at 90° is called perpendicular of that line. There are two methods to draw perpendicular of a line: Ruler and Set-Square Method. Ruler and Compasses Method. A perpendicular to a given line can be drawn such that the perpendicular passes through a point lies on the given line. A perpendicular to a given line can be drawn such that the perpendicular passes through a point outside the given line. A line which cuts another line into two equal parts at 90° is called perpendicular bisector of that line. The perpendicular bisector can be drawn to a given line segment using ruler and compass. An angle is a figure formed by two rays with the same initial point. The common initial point is called the Vertex of the angle. An angle of the given measurement can be constructed using protractor. An angle which is equal to the given angle, can be constructed using ruler and compass. The bisector of an angle is the line or line segment that divides the angle into two equal parts. The angle bisector of a given angle can be constructed using ruler and compass. Angles of given measurements (90°, 60°, 45°, 30°, 15° etc.) can be constructed without the help of protractor.

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