BASIC GEOMETRICAL CONCEPTS
Point – A point is an exact
location in space usually represented by a dot (.).
A point has no dimensions
(length & breadth).
Point A
Line – A line is a straight path
that extends without end in opposite directions.
Or, A line is a straight path of
points that extends endlessly in both the directions.
A line has no end points. It
does not have a definite length.
A line is named by using any two
points on a line.
•A •B
AB
BA
Line AB or line BA
Thus, the line
above is named as AB (line AB) or BA
(line BA).
Sometimes, a line is represented
by a small letters like
etc.
In the figure
given alongside
is line
There are two types of lines –
Straight line and Curved
line
Straight
lines are of three types –
Horizontal
line
Vertical line Slanting line
A curved line is called a curve.
Line
segment – A line segment is a part of a line that extends from one end point to
the other end point.
Or, A part of a line is called a
line segment. It has a fixed length that can be measured. The points at which
the line segment begins and ends are called its end points. Every line segment
has two end points.
•A
B•
AB line segment AB
Ray
– A ray is a part of a line which has one end point and extends without end in
one direction.
Or, A ray is a straight path
that has one end point and which extends endlessly in one direction.
•
•A AB or ray AB
Plane
– A plane is a flat surface which extends infinitely in all directions. Two
planes intersect in a line.
Or, A plane is a flat surface
that goes endlessly in all directions.
Collinear – Three or more points which lie on
the same line are called collinear.
•A •B •C •D
Angle – Two rays with a common end point form
an angle.
Or,
an angle is a figure formed by two rays with the same initial (end) point.
Ø The common end point is
called the vertex of the angle and the two rays the arms of the angle.
Ø An angle is also thought
of as a figure formed by rotating a single ray about its vertex.
A• O
or AOB or
BOA or O1 B•
Interior
and Exterior of an Angle –
Interior
– The inside of the angle, that is the region K •
Between the rays, is called the
interior of the angle. •X
•A
D•
Exterior
– The points of the plane that do not lie on the arms or L• E• Y• •M
in the interior of the angle are in the
exterior of the angle.
The
points x and y are in the exterior of ABC.
Ø Whenever two rays have a
common endpoint, we get an angle.
Kinds
of angles –
Angles are classified into
various types according to their measure.
1.
zero angle – An
angle whose measure is
is called zero angle.
2.
acute angle – An
angle whose measure is less than
but greater than
is called an acute angle.
Here,
P•
Q•
•R
3.
Right angle – An
angle whose measure is
is called a right angle.
4.
Obtuse angle – An
angle whose measure is between
is called an obtuse angle.
5.
Straight angle – An
angle whose measure is
is called straight angle.
6.
Reflexive angle – The
angle whose measure is between
is called a reflexive angle.
7.
Complete angle – An
angle whose measure is
is called a complete angle.
or, when the initial and terminal
positions of an angle coincide, the measure of the angle is called a complete
angle.
A complete angle is made up of two straight
angles.
Pairs of angles –
(i)Complementry
angle – Two
angles are complementary if their sum is
(ii)
Supplementry angle – Two
angles are supplementary if their sum is
.
(iii)Congruent
angle – Two
angles are congruent if their measures are equal.
Adjacent angle – Two
angles in the same plane that have a common vertex and a common side, but no
common interior points are called adjacent angles.
Parallel line – Two lines in the same
plane that never meet or intersect each other are called parallel lines.
Perpendicular
lines –
