Constructing the perpendicular from a point to a line

           When two lines intersect to form right angles then such lines are known as Perpendicular to each other. Perpendicular lines are Co-Planar (i.e., They lie in same plane) and intersect at right angle (90°).

Method 1: Constructing a perpendicular to a line through a point on it

1) Assume given line as AB and a point P is present near middle of the line on it,

2) Taking P as a center and any suitable radius on compass, draw an arc cutting line segment AB at two distinct points (C, D) as shown below

3) Taking C as centre and a suitable radius (more than CP or DP distance) draw an arc above the line segment, with D as centre and the same radius as previous, draw an arc cutting previously drawn arc,

4) Mark the intersecting point as E.

5) Join the points E and P as shown, and the line segment EP is the required perpendicular to line AB through point P.

Note: This method we follow when we don't have Protractor with us.

Manually Bisecting a Circular Arc

          In Geometry, bisecting an arc is cutting arc exactly in half.

Problem: To bisect an Arc

1. Draw an arc AB.

2. Draw a line (Chord) that connects the two points of the arc.

3. Set your compass more than half of the length of line and place compass on one end of the line ( or arc) and draw arc's above and below the arc AB.

4. Keeping the same distance set on your compass, swing arcs from another end of the line, draw arcs above and below the arc AB cutting previously drawn arc's.

5. Draw a line through the two intersection points of the arcs.

Bisecting an Angle

           An angle bisector divides an angle into equal angles. If the angle is 'θ', the two angles made after bisecting will be 'θ/2'. Angle bisectors can be constructed for an acute angle, obtuse angle, or a right angle too. This angle bisector passes through the vortex of an angle, as shown in the figure.

Problem: To bisect a given Angle ABC

1. Let us consider some angle ∠ABC, B as vortex,

2. Take some length in compass and place your compass on the vertex of the angle, here on point B. Draw an arc that crosses both sides of the angle, lines AB and BC. Mark those points as D,E as shown,

3. Place your compass on one of the intersection points (i.e., D) and draw an arc inside the angle. Do not adjust the compass,

4. Place your compass on the other intersection point (i.e., E) and draw an arc that cuts the previously drawn arc as shown,

5. Mark the intersecting point of arc's as F. Finally, draw a line connecting the vortex B and point F. This is the angular bisector of our angle ∠ABC.

6. You can measure both sides of the angle to check they are equal.

 

GEOMETRICAL CONSTRUCTIONS

          In this chapter, we deal with problems on Geometrical construction, which are mostly based on plane geometry and which are very essential in the preparation of Engineering Drawings.

They are:

1) Bisecting a Line

2) To draw Perpendiculars

3) To draw Parallel Lines

4) To divide a Line

5) To divide a Circle

6) To Bisect an Angle or Arc

7) To Trisect an Angle

8) To find the centre of an Arc

9) To construct an Ogee (or) Reverse curve

10) To construct Equilateral triangles

11) To construct Squares

12) To construct Regular Polygons

13) Special method of drawing Regular Polygons

14) Regular polygons inscribed in circles

15) To draw regular figures using T-square and set-squares

16) To draw Tangents

17)  Lengths of Arcs

18) Circles and Lines in contact

19) Inscribed Circles.

Bisecting a line

          In Geometry, Bisecting a line is cutting a line exactly in half. It may also be referred to as constructing a perpendicular bisector as the line you are drawing will be at a right angle to the original line. A line that passes through the mid point of the line segment is known as the segment Bisector.

Problem: To bisect a given straight line AB

1. Draw a straight line of given dimension and mark start and end points as A, B.

2.  To bisect this line, set your compass to just more than half the length of the line. Keep your compass this size for the rest of the question.

3. Place compass on one end of the line (i.e., point B) and draw an arc that crosses the line AB. Do not adjust the compass and keep the same length.

4. Place compass on the other end of the line (i.e., point A) and draw an arc. It must cut the other arc above and below the line. Mark the point of intersections as C,D.

5. Draw a straight line through where the two arcs intersect above and below the line (i.e., C,D). It will cut the line AB at O. CD bisects AB at right angles. 

6. Measure both sides of the line from 'O' check that they are of equal length, if they are equal we did it correctly.

Metric conversion table

 Metric conversion table

 AREA:

ha	Hectares	1 hectare = 2.47 acres or 1,07,639 square feet (sq ft)
sq.km	Square kilometre	1 sq. km = 0.386102 square mile (sq mi)

 LENGTH

km	Kilometre	1 km = 1000 m
m	Meter	1 m = 1000 cm
cm	Centimetre	1 cm = 1000 mm
mm	Millimetre	1 mm = 1000 µm
µm	Micrometre

  VOLUME

l	Litre	1 l = 0.001 m m3
m3 or cu.m	Cubic metre	1 m3 or cu.m = 10,00,000 cm3
cm3	Cubic centimetre	1 cm3 = 1e+21 Nm3
Nm3	Normal cubic metres
TEQ / Nm3	Dioxin toxic equivalent per  normal cubic  metres
KLD	Kilolitre per day

  MASS

MT or T	Metric tonne or tonne	1 MT or T = 1000 kg
kg	Kilogram	1 kg = 1000 g
g	Gram	1 g = 10,00,000 μg
μg	Microgram
gsm	Grams per square metre

  ENERGY

MW	Megawatt	1 MW = 1000 KW
kW	Kilowatt	1 KW = 1000 W
kcal	Kilocalories	1 kcal = 1000 cal

  TEMPERATURE

°C	Celsius	1°C = 33.800 Fahrenheit (°F)