Types of Diagrams
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A sketch is a rough diagram which does not have to be too accurate. A construction in mathematics is an accurate drawing done usually using only instruments such as a ruler as a straight edge, and a pair of compasses. |
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Perpendicular bisector
A perpendicular bisector, sometimes called a mediator, is a line which cuts another line in half and at right angles.
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To bisect AB at right angles: Step 1 Draw equal arcs, centres A and B, of radius more than half of AB to meet at P and Q. Step 2 Join P and Q. PQ is the perpendicular bisector of line AB
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Angle Bisector
An angle bisector, cuts or divides and angle in half.
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To bisect angle ABC: Step 1 Draw an arc, centre B, to cut AB at P, and BC at Q. Step 2 Draw equal arcs, centres P and Q, to intersect at R. Step 3 Join B to R. BR is the angle bisector of ∠'ABC |
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Parallel lines
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To construct a line parallel to AB passing through C. Step 1 Mark a point Q on the line AB. Step 2 Draw an arc, centre Q, radius QC, to cut AB at P. Step 3 Draw arcs with same radius, centres C and P, to intersect at R. Step 4 Join C and R. CR is parallel to AB |
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Perpendicular lines: Method A
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To construct a line perpendicular to AB passing through C: Step 1 Draw arc, centre C, to cut AB twice at P and Q. Step 2 Draw equal arcs, centres P and Q, to meet at R. Step 3 Join C and R. CR is perpendicular to AB |
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Perpendicular lines: Method B
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To construct a line perpendicular to AB passing through C: Step 1 Draw equal arcs, centre C, to cut AB twice atP and Q. Step 2 Draw equal arcs, centres P and Q, to meet at R. Step 3 Join C and R. CR is perpendicular to AB |
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Constructions from Given Data
Some shapes and figures can be drawn from given data such as lengths and angles using ruler and protractor .
Equilateral Triangle
Construct an equilateral triangle of side length 5 cm
Step 1 Draw an arc, length 5 cm, centre A
Step 2 Draw an arc from a point B, to cut the original arc at C.
Step 3 Join ABC
ABC is an equilateral triangle
Quadrilateral
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Draw a quadrilateral ABCD, with angle A = 110° and angle B = 80° and sides of AD = 4 cm, BC = 5 cm and base AB = 6 cm. Step 1 Draw the line AB of length 6 cm. Step 2 Set compasses to 4 cm and draw arc on A. Step 3 Set compasses to 5 cm and draw arc on B. Step 4 Use protractor to draw angles of 110° and 80° on A and B Step 5 Join the four points. |
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Hexagon
Construct a regular hexagon
Step 1 Draw a circle
Step 2 Set compasses to 5 cm and draw arc on A.
Step 3 Continue working round circle making arcs of 4 cm.
Step 4 Join each point of intercection of the arcs with the circle together.
Triangles
Two constructions in triangles that are often required are:
The medians of a triangle are lines from each vertex to the middle of the opposite side.
The altitudes of a triangle are lines from each vertex which meet the opposite side of the triangle at right angles.
