WELCOME

WELCOME TO MATHS PROJECT WORK

DONE BY : PRABHAT.G.P

GUIDED BY :RADHA MAM

MATHEMATICS

• UNIT-5• BASIC GEOMETRICAL CONCEPTS {2D} Geometry is a branch of mathematics which deals with length, breadth, and height of different shapes. The word ‘Geometry’ is derived from the Greek word ‘Geo’ means earth and ‘metric’ means measurement.

LINE SEGMENT

BASIC GEOMETRICAL CONCEPTS

• Line segment Fold a piece of paper , press it by finger tip to form a crease and then unfold it as shown in the figure. What do you observe? You observe that a crease is formed. This is a line segment.

LINE SEGMENT

• y z YZ is a straight line segment. Note: A straight line segment has only one dimension, i.e. length. It has no width or thickness.

RAY

1. WHAT IS A RAY?

ANS: A line segment which extends endlessly in one direction from a starting point is called a ray.

RAY

• These are the rays from the sun.

SUN

LINE SEGMENT,LINE AND RAY

LINE SEGMENT LINE RAY

It has two end points. A straight line has no end points.

A ray has one starting point.

A B AB represents line segment.

A BAB represents straight line.

A B AB represents ray.

The length of a line segment is finite.

The length of a straight line is infinite.

The length of a ray is infinite.

AB and BA represent the same line segment.

AB and BA represent the same line.

AB represent different ray.

OPEN AND CLOSE FIGURES

• SHAPES OF OPEN FIGURES.

• SHAPES OF CLOSED FIGURES

Circle Star Square Ellipse

OPEN AND CLOSED FIGURES.

1. WHAT ARE CALLED OPEN FIGURES?ANS: Figures with straight line or curved line which do not end at the starting point is called an open figure.

2. WHAT ARE CALLED CLOSED FIGURES?ANS:Figures with straight line or curved line which ends at the starting point is called a closed figure.

GEOMETRIC NAMES

1. WHAT ARE THE GEOMETRIC NAMES FOR THE FIGURES?ANS: In general, figures , polygons, polyhedrons, shape, irregular, regular …… Other examples: circle, triangle, square, quadrilateral, rectangle, rhombus, parallelogram ……etc. are Geometric names of figures.

2. WHAT IS A GEOMETRIC NAME FOR A FIGURE THAT HAS FOUR SIDES?ANS: Quadrilateral is the name for geometric figure with four sides.

1. HOW MANY TYPES OF CLOSED FIGURE ARE THERE? NAME THEM?

Ans: There are three types of closed figures are there. They are:a) INTERIOR OF A CLOSED FIGURE.b) EXTERIOR OF A CLOSED FIGUREc) BOUNDARY OF A CLOSED FIGURE

CLOSED FIGURES

INTERIOR OF CLOSED FIGURE

2. WHAT IS INTERIOR OF THE CLOSED FIGURE?Ans: The shaded part inside the figure is called “ interior of the closed figure”.

EXTERIOR OF THE CLOSED FIGURE

3. WHAT IS EXTERIOR OF THE CLOSED FIGURE?Ans: The outer portion of the figure is called “exterior of the closed figure”. a

b c

4. WHAT IS BOUNDARY OF THE FIGURE?Ans: The points on boundary of the figure is called the boundary of the figure. A

B C

BOUNDARY OF THE CLOSED FIGURE

LINEAR AND CURVILINEAR BOUNDARIES

1. WHAT IS CURVILINEAR BOUNDARY?GIVE FIGURES?Ans: The boundary of closed figure have curved lines. So the boundary having a curved line is called “curvilinear boundary”.

LINEAR AND CURVILINEAR BOUNDARIES

2. WHAT IS LINEAR BOUNDARY? GIVE FIGURES?Ans: The boundary of closed figures are made up of line segments. So a boundary containing only line segments or straight lines is called linear boundary.

INTERIOR AND EXTERIOR OF AN ANGLE

• NOTE • The interior of an angle is not a line segment

area. It extends indefinitely since the two sides extend indefinitely.

INTERIOR AND EXTERIOR OF AN ANGLE

a x p q r c y z b

INTERIOR AND EXTERIOR OF AN ANGLE

IN THE GIVEN FIGURE:• THE POINTS P,Q,R LIE ON THE

INTERIOR OF AN ANGLE.• THE POINTS A,B,C LIE ON THE

EXTERIOR OF AN ANGLE.• THE POINTS X,Y,Z LIE ON THE

BOUNDARY OF AN ANGLE.

TRIANGLES – VERTICES – SIDES AND ANGLES

A

B C A Triangle is a closed figure bound by three line segments. The symbol for triangle is . So triangle ABC is written as ABC. The line segments AB, BC, AC are called sides of the triangle. Similarly B and C are also vertices.

ALTITUDE AND MEDIAN OF A TRIANGLE

1. WHAT IS ALTITUDE OF A TRIANGLE?Ans: The perpendicular line segment drawn from a vertex of a triangle to its opposite side is called ‘altitude’ of the triangle. Altitude is also called as ‘ height’ of the triangle. AX is called the altitude of ABC A

B X C

MEDIAN

P

Q D R The line segment drawn from a vertex of a triangle to the mid of its opposite side is called ‘a median’

QUADRILATERALS – SIDES – ANGLES, AND VERTICES.

S R

P Q NOTE: QUAD MEANS FOUR AND LATERAL MEANS SIDE

QUADRILATERAL

1. WHAT IS A QUADRILATERAL?Ans: A Quadrilateral is a plane closed figure bounded by four line segments. NOTE:The point of intersection of sides of a quadrilateral is called a ‘vertex’ of the quadrilateral.

DIAGONAL OF QUADRILATERAL

S R

P Q2. WHAT IS DIAGONAL?Ans: The line segment joining the opposite vertices of a quadrilateral is called a diagonal

ADJACENT AND OPPOSITE SIDES OF A QUADRILATERAL

• The pair of sides which have common end point are called ‘adjacent sides’ of a quadrilateral.• The other name for adjacent sides is consecutive sides

INTERIOR AND EXTERIOR OF A QUADRILATERAL

D C P L Q R M

A N B

INTERIOR AND EXTERIOR OF A QUADRILATERAL

• THE REGION BOUNDED BY FOUR SIDES OF A QUADRILATRAL IS CALLED THE ‘INTERIOR OF THE QUADRILATERAL’.

• THE REGION OUTSIDE THE BOUNDARY OF THE IS CALLED THE ‘EXTERIOR’ OF THE QUADRILATERAL .

1. DEFINE ANGLE. GIVE FIGURES.Ans: An Angle is formed by two rays starting from a common point. a

b c

ANGLES – VERTEX - ARMS

ANGLES - ARMS - VERTEX

2. WHAT ARE ARMS?Ans: The two rays are called arms. Arms are also called ‘ sides’3. WHAT IS VERTEX?Ans: The common fixed point is called vertex of an angle.

ANGLES

1. HOW MANY TYPES OF ANGLES ARE THERE?

ANS: THERE ARE SEVEN TYPES OF ANGLES. THEY ARE

a) ACUTE ANGLE (0 TO 90 degree)b) RIGHT ANGLE (90 degree)c) OBTUSE ANGLE (90 TO 180 degree)d) STRAIGHT ANGLE (180 degree)e) REFLEX ANGLE ( 180 to 360 degree)

ANGLES

f) COMPLETE ANGLE ( 360 degree)g) ZERO ANGLE ( 0 degree)

ANGLES

1.a) WHAT IS ACUTE ANGLE ? ANS: AN ANGLE WHICH IS MEASURES MORE

THAN 0 DEGREE AND LESS THAN 90 DEGREE IS CALLED ACUTE ANGLE .

A

B C

ANGLES

• 1. b) WHAT IS RIGHT ANGLE ?ANS: AN ANGLE WHICH 90 DEGREE IS CALLED

RIGHT ANGLE. A

B C

ANGLES

1.c) WHAT IS OBTUSE ANGLE ?ANS: AN ANGLE WHICH MEASURES MORE THAN 90 DEGREE AND LESS THAN 180 DEGREE IS CALLED OBTUSE ANGLE. P

Q R

ANGLES

1.d) WHAT IS STRAIGHT ANGLE ? ANS: AN ANGLE WHICH IS MEASURES EXACTLY 180 DEGREE IS CALLED STRAIGHT ANGLE.

A B C

ANGLES

1. e) WHAT IS REFLEX ANGLE ? ANS: AN ANGLE WHICH MEASURES MORE THAN 180 DEGREE BUT LESS THAN 360 DEGREE IS CALLED REFLEX ANGLE.

ANGLES

1.f) WHAT IS COMPLETE ANGLE?ANS: AN ANGLE WHICH MEASURES 360 DEGREE IS CALLED COMPLETE ANGLE.

ANGLES

1.g) WHAT IS ZERO ANGLE?ANS: AN ANGLE WHICH MEASURES 0 DEGREE IS CALLED ZERO ANGLE.

CIRCLE – CENTRE, RADIUS AND DIAMETER

• A Circle is a closed plane figure such that all its points are equidistant from a fixed point on the plane. The fixed point is called ‘Centre of a circle’

• The fixed point is known as ‘Centre’ of the circle. The constant distance is called the radius of a circle

RADIUS OF A CIRCLE

D A C BThe line segment joining the centre to any point on the circle is called the ‘radius’ of the circle.

DIAMETER OF A CIRCLE

C

A B D The line segment which passes through the centre of a circle and whose end points lie on the circle , is known as the ‘diameter’ of a circle. Diameter is denoted as ‘d’.

T

CHORD OF A CIRCLE

E

C D

B A F

CHORD OF A CIRCLE

• A Line segment joining any two points on the circle is called a ‘chord’.

• X is the centre of a circle.

• AB, AE, CD, EF, CF ARE CHORDS.

ARC OF A CIRCLE

X

Y

ZPart of a circle between X and Z is called an ‘arc’. An Arc is denoted by

L

SEGMENT OF A CIRCLE

P Q R

QThe region enclosed by an arc and a chord of a circle is called a ‘segment’of the circle.

M

SECTOR OF A CIRCLE

• L

K P N

The region enclosed by an arc and a pair of radii of a circle is called a ‘sector’ of the circle.

K

SEMI - CIRCLE

A

L M

B

H

SEMI - CIRCLE

Diameter divides the circle into two segments LAM and LBM. They are equal. They are half squares. A half circle is known as a semi - circle

CIRCUMFERENCE OF THE CIRCLE

THE PERIMETER OF A CIRCLE IS CALLED A ‘CIRCUMFERENCE’ OF A CIRCLE.

THANK YOU

GUIDED BY : RADHA MAM DONE BY : PRABHAT.G.P