Geometric Constructions Tutorial

Geometric constructions is a basic construction of geometric figures. In this article we can see the construction of a perpendicular bisector, construction of an angle and construction of a triangle. For the construction of geometric figures we use only the help of a ruler (straight-edge) and compass. Compass is generally used to draw arcs of particular distances. The distance is calculated with the help of a ruler.
Geometric Constructions

i) To bisect a given line segment

Given: A line segment AB

To construct: The perpendicular bisector AB

Construction:      a) With A as centre and radius equal to more than half of AB, draw two arcs, one on each side of AB.

b) With B as centre and with the same radius taken above draw two more arcs cutting the previous arcs                              at C and D

c) Join C and D cutting AB at O. CD is the perpendicular bisector of AB.

perpendicular bisector of a line segment

ii) To construct an angle of 60°

Construction: a) Draw a line segment AB of any suitable length.

b) With A as centre and any suitable radius draw an arc cutting AB at C.

c) With C as centre and the same radius AC, draw another arc cutting the former arc at D.

d) Join A and D and produce it to E.
construction of angle 60degrees

iii) To construct an angle of 30°

Construction: a)First construct an angle of 60° as shown above

b) With C and D as centre, draw two arcs of equal radii cutting each other at F

c) Join A to F.
construction of angle 30degrees

Construction of more Geometrical Shapes

iv) To construct a triangle having given the lengths of three sides.

Let the three sides be 3.6cm, 4cm and 5.1cm

Construction: a) Draw a line segment AB = 3.6cm

b) With A as centre and radius = 4cm, draw an arc.

c) With B as centre and radius = 5.1cm draw one more arc intersecting the former arc at C.

d) Join AC and BC. Then ΔABC is the required triangle.(Note: The construction fails when the sum of any two sides is less than the third side.)

Algebra is widely used in day to day activities watch out for my forthcoming posts on Combinations and Permutations Examples and Continuity of a Function. I am sure they will be helpful.

v) To construct a triangle, having given the lengths of any two sides and the included angle.

Let the length of the two sides be 3.9cm and 4.3cm and included angle be 60°

Construction:a) Draw a line segment AN = 3.9cm

b) Construct
c) From AX, cut off AC = 4.3cm

d) Join BC. Then ΔABC is the required triangle.

construction of a triangle, where two sides and included angle are given