6.1
Introduction:
Geometry is that branch of mathematics which
studies the properties of figures such us lines, triangles, quadrilaterals etc.
Ancient Indians used the geometrical properties for
construction of fire places called ‘yajnakundas’.
They also had profound knowledge of
astronomy, as even today the method of calculation
of occurrences of eclipses are precise and date and times are arrived at
many years in advance of their occurrence.
1.
Can you divide the below mentioned line segment in to two
exact parts without using the scale?
2.
What should be the size of underground tank to store
petrol/milk and water supplied through tankers?
3.
Why do people who prepare sweets, makers cut the ‘burfi’
in the shape of parallelograms rather than rectangulars?
In geometry we find answers/solutions to above mentioned concepts/problems.
6.1.0 Definitions and some basic constructions:
Definition:
‘Angle’ is a figure formed by two rays with a common end point.
They are measured in degrees (0^{0} to 360^{0}) The
common end point is called ‘vertex’. In
the above figure B is a vertex; ABC is an angle and is denoted by _{}ABC. When we measure
with protractor, we get _{}ABC = 50^{0}. Note _{}ABC =_{}CBA = 50^{0} 

No 
Type of
angle 
Measure
of angle is 
Example
in the adjacent figure 

1 
Acute Angle 
Between 0^{0} and 90^{0} 
_{}AOC 

2 
Right Angle 
= 90^{0} 


3 
Obtuse Angle 
Between 90^{0} and 180^{0} 
smaller _{}COB (clock wise direction) 

4 
Straight Angle 
= 180^{0}( Angle on
straight line) 
_{}AOB 

5 
Reflex Angle 
Between 180^{0} and 360^{0} 
Larger _{}BOC ( clock wise
direction) 
6.1.1. Construction of Perpendicular to a line from a point.
Step
1: Draw the line AB of given measurement and C be an external point. Step 2: With C as center, draw
an arc of suitable radius to cut the line AB at 2 points (If necessary extend the line)
X, Y as shown in the figure. Step 3: With X and Y as centers,
draw arcs (of radius more than half of XY) to cut at point Z on the other side of AB. Step 4: Join C, Z to intersect
the line AB at L CL is perpendicular to AB. Note: The procedure for
construction of perpendicular at a point on the line is same as above. (C
could be a point like L on AB) 

Note: Using SSS and SAS postulate (Refer Section
6.4.3), you can prove that _{}CLY =_{}CLX = 90^{0})
6.1.2. Construction of Perpendicular bisector to a line.
Step1
: Draw the line AB of given measurement. Step2: With A, B as centers,
draw arcs of radius more than half the length of AB on both sides of AB. Let
these arcs meet at X and Y. Step3: Join XY to meet AB at L. (Note that XY bisects AB and XY
is perpendicular to AB and L is mid point of AB) 

Note: Using SSS and then SAS postulate (Refer
Section 6.4.3), you can prove that
6.1.3. Construction of Angular bisector.
Step1: construct _{}CAB of given measurement using protractor. Step2: With A as center, draw
arcs of same radius to cut the sides AB and AC at P and Q respectively. Step3: With P and Q as centers
as and with more than half of PQ as radius, draw arcs to intersect at R. Step4: Join 

Note: Using SSS postulate (Refer Section 6.4.3), you
can prove that _{}CAR =_{}RAB)
Locus is the path traced
by a moving point, which moves so as to satisfy the given
condition/conditions. An example is the circumference of a circle. Any point on a circumference is at equal
distance from the center of the circle. Thus circumference is locus of circle. 

6.1 Summary of learning
No 
Points learnt 
1 
Definitions
and basic constructions 