GEOMETRY GEOMETRY PRESENTATIONPRESENTATION

PRESENTED BY:

SHAGUFTA KHAN

SHAPES

LINESANGLES

Types of Triangle

Spec

ial 4

si

des

Area andMeasurement

isosceles

triangleequilateral

Right

square

rectangular trapeziumcircle Rhombu

s

h

base Base area=1/2*base*height

rectangular

Square

Rhombus

parallelogram

What did the acorn say when he grew up?

Points Lines Planes

Circles PolygonsCongruency

Similarity

ContentIntroduction.Objectives/Importance.Curriculum Alignment.Basic Geometrical Concepts.Construction of Triangle.Area of Triangle.Activities to teach.Misconception and Issue.

CURRICULUM ALLIGNMENT

Shapes, its kinds and classificationLines, Angles and its types.Measurements( Area and

Parameter)Use of Protractor and Scale to

measure.

What is Geometry &

their IMPORTANCEGeometry is the study of shapesThey studied Geometry in Ancient Mesopotamia & Ancient EgyptGeometry is important in the art and construction fields

INTRODUCTION

Plane Geometry is about flat shapes like lines, circles and triangles ... shapes that can be drawn on a piece of paper

 

Solid Geometry is about three dimensional objects like cubes, prisms, cylinders and spheres.

Point, Line, Plane and SolidA Point has no dimensions, only positionA Line is one-dimensionalA Plane is two dimensional (2D)A Solid is three-dimensional (3D)  Ray: A line with a start point but no end point

LINES• STRAIGHT LINE: A line with

constant direction.• CURVED LINE: A line that is bent

without an angle.

OPEN & CLOSED FIGURES

• A CLOSED FIGURE/SHAPE starts and ends at the same point.

• An OPEN FIGURE/SHAPE does NOT start and end at the same point.

CLOSED OPEN

●●

●

Start

End

Start

End

ACTIVITY 1

If a line is cute at two parts, then the part of a line between the cuts is called ‘LINE SEGMENT’. It has two end points.

Line segmentLINE SEGMENT

Line segmentA B

PARALLEL AND PERPENDICULAR LINES

• PARALLEL LINES: Two equal distance lines that never meet each Othereven if they stretched unlimited.

PERPENDICULAR LINES: Lines that are at right angles (90°) to each other

MEASURING LENGTH• You can measure how long things are,

or how tall, or how far apart they are. Those are all examples of length measurements.

Example: This fork is 20 centimeters long

ANGLE

• The two straight lines that have a common end is called angle.

HOW MANY ANGLES DOES EACH HAVE?

COMPLEMENTARY ANGLE

• Two angles are complementary if the sum of their angles equals 90o. If one angle is known, its complementary angle can be found by subtracting the measure of its angle from 90o.

• Example: What is the complementary angle of 43o? Solution: 90o  -  43o  =  47o

SUPPLIMENTARY ANGLE• Two angles are supplementary if the

sum of their angles equals 180o. If one angle is known, its supplementary angle can be found by subtracting the measure of its angle from 180o.

• Example: What is the supplementary angle of 143o? Solution: 180o  -  143o  =  37o

DIFFERENT TYPES OF ANGLE• Acute Angle an angle that is less than 90° • Right Angle an angle that is 90° exactly • Obtuse Angle an angle that is greater than

90° butless than 180°

• Straight Angle an angle that is 180° exactly • Reflex Angle an angle that is greater than

180°

AREA• Surface of any shape/figure, covered

by lines is called area.

FINDIND AREA ( LxB)FINDIND AREA ( LxB)Question: LOOK AT THE FOLLOWING FIGURE AND GIVE THE AREA IN SQUARE Cm2

PERIMETERThe distance around a two dimensional shape.

The perimeter of this regular pentagon is 3+3+3+3+3 = 5×3 = 15

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The perimeter of this rectangle is 7+3+7+3 = 20

MEASUREMENT OF PERIMETER

• RectangleArea = w × hw = widthh = height

• SquareArea = a2

a = length of side

• SquareArea = a2

a = length of side

SHAPES WITH SAME AREA CAN HAVE DIFFERENT PERIMETER

2cm

2cm

1cm

1cm

AREA=4cm

2

Perimeter=8cm

Area=6cm 2

Perimeter= 10cm

HERE IS THE SITE PLANE OF A HOUSE. FIND AREA AND

PERIMETER?

Circle• In a plane, each point of the circle is at equal

distance from a fixed point. The fixed point is called the centre of the circle.

• The distance from centre to any point on the circle is called radius of the circle.

• A Line segment passing through the centre of the circle and whose end points lie on the circle is called the diameter of the circle.

• The length of the circle or the distance around it is called circumference of the circle.

0circle

Radius

Diameter

D=2r

circumference

Using a Protractor• Helps you measure angles (in degrees)• Protractors usually have two sets of

numbers goingin opposite directions

• Each row of half• Protractor=180°

KINDS OF TRIANGLE

Constructing a triangle given SASHow could we construct a triangle given the lengths

of two of its sides and the angle between them?

side

side

angle

The angle between the two sides is often called the included angle.

We use the abbreviation SAS to stand for Side, Angle and Side.

Constructing a triangle given ASAHow could we construct a triangle given two angles and the length of the side

between them?

The side between the two angles is often called the included side.

We use the abbreviation ASA to stand for Angle, Side and Angle.

side

angleangle

Constructing a triangle given SSS

How could we construct a triangle given the lengths of three sides?

side

We use the abbreviation SSS to stand for Side, Side, Side.

side side

Hint: We would need to use a compass.

Constructing a triangle given RHSRemember, the longest side in a right-angled triangle is called the hypotenuse.

We use the abbreviation RHS to stand for Right angle, Hypotenuse and Side.

How could we construct a right-angled triangle given the right angle, the length of the hypotenuse and the length of one other side?

hypotenuse

right angleside

Examples• 1 What is the area of this square?• Solution• Area = s × s• = 3.2 × 3.2• = 1024 cm2

• 2 What is the area of this rectangle?• Solution• Area = l × b 6 cm = 60 mm• = 60 × 5• = 300 mm2

Areas of composite shapes• Find the area of this shape.• Solution• Method 1• Area of shape = area of rectangle Y +

area of square X• = (6 × 2) + (3 × 3)• = 12 + 9• = 21 cm2

What about this shaded area?

• Area of purple shape = area of big rectangle − area of small rectangle

• = (75 × 45) − (32 × 24)• = 3375 − 768• = 2607 mm2

• What shapes can you see?

• Solution• Divide the shape into a triangle and a rectangle.• Area of shape = area of rectangle + area of

triangle• = (16 × 14) + (½ × 14 × 14)• = 224 + 98• = 322 cm2

224cm2

A = ½bh

98cm2

MISCONCEPTIONS IN GEOMETRY

•Identifying the Base and Height of a

Triangle.•Conservation Misconception •Angles: Larger Space means Larger Angle •Shape Properties •Orientation and Rotation of Shapes •Perpendicular lines •There Are Four Sorts Of Triangle: Scalene,

Isosceles, Equilateral And Right-Angled

Thank you

Once you study all the “fancy words”, Geometry is very easy to understand…so STUDY!