Introduction
This chapter deals with some of the important basic construction techniques frequently used in Engineering Drawing.
Geometric Terms Triangle
A triangle has three sides; the sum of its angles is equal to 180º.
Equilateral Triangle
An equilateral triangle is a triangle, which has three equal sides.
AB = BC = CA
∠ABC = ∠BCA = ∠CAB = 60°
Right-Angled Triangle
In a right-angled triangle, the included angle between two of its sides is equal to 90º.
∠ABC = 90º
Isosceles Triangle:
An isosceles triangle is a triangle, which two sides, and two angles are equal.
AB=AC and ∠ACB=∠ABC
A
A B
A quadrilateral has four sides; the sum of all its angles is equal to 360º.
Square
When all the sides of a quadrilateral are equal and all its internal angles are right angles, the quadrilateral is called a square.
AB = BC = CD = DA
Rectangle
When the opposite sides of a quadrilateral are equal and all its internal angles are right angles, the quadrilateral is called a rectangle.
AB = CD and BC = AD
Rhomboid
When the opposite sides and angles of a quadrilateral are equal and none of its angles are right angles, the quadrilateral is called a rhomboid.
AB = CD BC = AD
∠=ABC= ∠=CDA and ∠=BCD= ∠=DAB
Rhombus
When all the sides of a quadrilateral are equal and none of its internal angles are right angles, but the opposite angles are equal, the quadrilateral is called a rhombus.
AB = BC = CD = DA
Trapezoid
When two opposite sides of a quadrilateral are equal and the other two opposite sides are parallel, the quadrilateral is called a trapezoid.
AB = CD AD || BC
Trapezium
When no side of a quadrilateral is parallel or perpendicular to any of its other sides, the quadrilateral is called a trapezium.
Parts of a Circle Arc
The part of a circle between any two points on its circumference is called an arc.
Arc = AB
Segment
The part of a circle bounded by an arc and a chord is called a segment.
Segment = ABC
Chord
A straight line joining any two points on the circumference of a circle is called a chord.
Chord = AB
Sector
The part of circle bounded by two radii and an arc is called a sector.
Sector = DEF
Polygons
Types of Polygons
A plane figure bounded by straight lines is called a polygon. Polygons are classified into two types. They are:
1. Regular Polygon 2. Irregular Polygon
Regular Polygon
A polygon in which all the sides and all the angles are equal is called a regular polygon.
Chord
Sector F D
E
F D
E
Chord A
B
Pentagon:
A regular pentagon has five equal sides. Its angles are equal. The internal angle of a regular polygon of "n" sides= {(2n-4) 90°}/n. The internal angle of a regular pentagon = 108°
AB = BC = CD = DE = EA
Hexagon:
A regular hexagon has six equal sides. Its angles are equal. The internal angle of a regular hexagon =120°
AB = BC = CD = DE = EF = FA
Heptagon:
A regular heptagon has seven equal sides. Its angles are equal. The internal angle of a regular heptagon = 128.57°
Octagon
A regular octagon has eight equal sides. Its angles are equal. The internal angle of a regular octagon = 135°
AB=BC=CD=DE=EF=FG=GH=HA
Nonagon
A regular nonagon has nine equal sides. Its angles are equal. The internal angle of a regular nonagon = 140°
AB=BC=CD=DE=EF=FG=GH=HI=IA
Decagon
A regular decagon has ten equal sides. Its angles are equal. The internal angle of a regular decagon = 144°
AB=BC=CD=DE=EF=FG=GH=HI=IJ=JA
Irregular Polygon
The sides and angles of an irregular polygon are unequal. Hence irregular polygons are not used in engineering drawing.
A B
Geometric Construction:
To Bisect a Line:
1. Draw the given line AB.
2. With A as centre and radius greater than half AB, draw arcs on both sides of AB.
3. Similarly with B as centre and the same radius, draw arcs to intersect the previous arcs at C and D.
4. Join C and D. The line AB is now bisected.
To Bisect an Arc:
1. Draw the given arc AB.
2. With A as centre and a radius greater than half AB, draw an arc on both sides of AB.
3. Similarly with B as centre, and the same radius draw arcs to intersect the previous arcs at C and D.
4. Join C and D. The arc AB is now bisected.
D o C
D C
D
B A
C
D
A B
To find the centre of an arc:
1. Draw the given arc AB.
2. Draw two chords PQ and RS of any length within AB.
3. Bisect the chords.
4. Let the bisectors intersect at O; then O is the centre of the arc.
To Bisect an Angle:
1. Draw the given angle ABC
2. With B as centre and any radius, draw an arc cutting AB at D and BC at E
3. With D and E as centres and the same or any other radius, draw arcs within the angle to intersect each other at F
4. Join B and F. The line BF divides the angle ABC equally, or "bisects" it.
A
B
P Q
R
s O
D
E F A
B C
To construct a regular Pentagon:
1. Draw a line BA equal in length to the given side of the pentagon.
2. At B, draw a line at an angle of 108º (angle of regular polygon of "n" sides= {(2n-4) 90°}/n) to AB.
3. Similarly at A draw a line at angle of 108º to AB.
4. With B as centre and radius equal to AB draw an arc on the first line to cut it at C (AB=BC).
5. Similarly, with A as centre and radius AB draw an arc on the second line to cut it at E (BA=AE).
6. With C and E as centres and radius equal to AB draw arcs to intersect at D.
7. Join CD and ED. ABCDE is the required pentagon.
108 108
A B
C E
D
A B 120 0120 0
F C
E D
60 0 60 0
To Construct a regular Hexagon:
1. Draw a line AB equal in length to the given side of the hexagon.
2. Draw perpendiculars at A and B.
3. Draw two lines at 120° to AB, one at the left of A and another one at right of B.
4. With A as centre and the radius equal to AB, draw an arc on the second line to cut it at F.
5. With B as centre and radius equal to AB, draw an arc to cut the first line at C.
6. With C and F as centres and equal to AB cut the perpendiculars at D and E.
7. Join CD, FE and ED. ABCDEF is the required hexagon.
To construct a regular Octagon:
1. Draw a line BA equal in length to the given side of the octagon.
2. Draw perpendiculars at A and B.
3. Draw two lines at 135° to AB, one at the left of B and the other one at the right of A.
4. With B as centre and radius equal to AB, draw an arc to cut the first line at C.
5. With A as centre and the same radius (=AB), draw an arc on the second line to cut it at H.
6. Through C and H draw lines parallel to the perpendiculars at A and B.
7. Using compasses draw CD and HG equal to AB.
8. With G and D as centres and radius equal to AB cut the perpendiculars (at A and B) at F and E.
9. Join DE, EF and FG. ABCDEFGH is the required octagon.
135 135
B A C
D
H G E F
GENERAL CONSTRUCTION METHOD OF POLYGON:
C D
E
O