The application of geometery

1. ry
basicsof geometry
Presented To:
Mam Ayesha Noreen
Department of
Biotechnology
Faculty of Applied
Sciences
Sr .No Name Roll No
1 Wasifa Neha 1
2 Saifa Malik 2
3 Samra Sajid 3
4 Zara Pervaiz 4
5 Muhammad ATEEQ 5
6 Momal Wajid 6
7 Zammad Naseer 7
8 Raheel Khalil 8
9 Tayyaba Afzal 9
10 Iman shehzad 10
PresentedByGroup1st

2. Geometry
:
This word is actually derived from the Greek word
‘geometron’. Now, ‘geometron’ is actually made of
two words – Geo and Metron. So geometry is the
mathematical study of all shapes and figures. It
can be seen everywhere in our everyday life. We
live in a world of shapes and here we shall see
how mathematics helps us understand the basics
of geometry

3. 1.1:
Point
A point is an exact location on the plane. It has no size. It is denoted by the capital letter of the
English alphabet.
Collinear and Non- Collinear Points
Points which lie on the same straight line are collinear points. The points
which don’t lie on the same straight line are non-collinear points.
Ray
Now we will discuss what is meant by a ray. What comes to your mind when
you think of the ray? Sun rays right? We know that the sun rays start from the
sun and goes on endlessly. That means it has the starting point but it has no
endpoint. So this nothing but a ray.

4. Point
Ray

5. 1.2: Line
A line is a straight path that is
endless in both directions. That
means it extends in both
directions without end.
Line Segment:
A line segment is a part of a line.
The main difference the line and
the line segment is that lines do
not have endpoints while line
segments have endpoints.

6. 1.3:Plane
The plane is a
two-dimensional
surface. A plane has
length and width, but
no height, and extends
infinitely far on all
sides. It is made up of
made up of an infinite
amount of lines.

7. 1.4:Angles
Angle is the combination of
two rays with a common
endpoint. The symbol for an
angle is ∠. The corner point
of an angle is called the
vertex of an angle. The two
straight sides of the angle
are the arms of the angle

8. A: parallel Lines
1-5 parallel and Intersecting lines
W hen the distance
btw a pair of lines is
always same, then
we call such lines as
parallel lines.

9. B:Intersecting Lines
Lines that
intersect each
other at one point
are something we
call as
intersecting lines.

10. 1.3: Verticies and
Angles
Vertex
A vertex is a point where
two or more lines, line
segments, or rays intersect
(cross or connect with)
each other. Since a vertex
is a point, it follows the
same naming guidelines as
points. This would be
called vertex A.

11. Angle
An angle is formed by two rays
with the same endpoint (the
vertex).
They can be named by drawing
the angle symbol <
followed by the vertex point, by
naming all 3 points involved in
the angle, with the vertex in the
center, or by using a numerical
name assigned to a particular
angle.

12. 1.4: Polygons
polygon is a closed two-dimensional figure on a
plane with at least three straight sides and no
curved sides. Essentially, it's any two dimensional
shape without curves. So a triangle is a polygon,
but a circle is not.
Shapes with equal length sides and interior angles
are known as regular and irregular polygons.
An interior angle is an angle formed on the inside
of a polygon where two sides meet.

14. Polygons By Number of
Sides
Triangle
A triangle is a
polygon with three
sides.
The three angle
measurements
angles of a triangle
add up to 180°.

15. Quadrilateral
A Quadrilateral is a
polygon with four
sides.The four
interior angle
measurements of a
quadrilateral add up
to 360°

16. Pentagon
A Pentagon is a
polygon with five
sides.
The five interior
angle measurements
of a pentagon add up
to 540°

17. 1.5 Circles
• A circle is closed two dimensional figure in which the set of
all points in the plane is equidistant from a given point called
center.
• The first theorm relates to circle are attributed to [Thales]
around 660 BC.
• There are 3 main pasts of circle the diameter, center and
radiud
Types
• Tangent circle
• Concentric circle
• Congruent circle

18. Properties of circle
• The circle are said to be congruent if they have
equal radii.
• The diameter of a circle is longest chord of
circle.
• Circle having different radius are similar
• Equal chords of a circle substend equal anles
at the center
• The radius drawn perpendicular to chord
bisects the chord.