Parallel lines, perpendicular lines, geometry

Hello children, in this session we will discuss about one of the most interesting topics of mathematics- geometry . First question that arises in mind is, what is geometry? When we study about shape and size of a figure in space than this study is called as a geometry. For insrance, a persaon draws a figure of his house and then analyzes that figure. This process of analyzing figures is known as a geometry.

Fundamentals of geometry -

Point and line are two fundamentals concepts of geometry. When you touch the tip of your pen on paper then a dot is made. This dot is a point. For understanding the definition of a point, have a look at the figure below:

This figure is called as point . So, we can say that point is a dimensionless location in space (here dimensionless means there is no length , no height and no width .)
The next fundamental concept of geometry is a line . When we join two points , one figure is created and this figure is called as a  line .
A <-----------------------------------------> B
AB is a line.
There are two type of lines in space –

1. Parallel lines
2. Perpendicular lines
   

Parallel Lines Definition : Two lines which never meet in space , then these two lines are known as a Parallel lines or in other word two lines which always  maintain same distance between them are said to be Parallel lines.

In the figure, line1 and line2 are patallel to each other. One can observe that the didtanve between two lines is always same.
Now, we will discuss properties of Parallel lines . These lines have following  properties –

• Parallel lines never intersect each other.
• Distance between parallel lines always remains constant for each and every point .
• Parallel lines always remain in same plane .
  

Perpendicular lines  :  Two lines which intersect with each other at right angle i.e. intersect at 90 degree angle are called as perpendicular lines .

In the figure line 1 and line 2 are perpendicular to each other and meet at point O. Point O is called the point of intersection of the perpendicular lines.

perpendicular lines have following properties –

• Perpendicular lines always intersect each other at 90 degree .
• Perpendicular lines always remain in same plane .

So, this is all about geometry portion of grade IV .

In upcoming posts we will discuss about Symmetry of geometric figures and grade V. Visit our website for information on Andhra Pradesh geography questions

Understand various Angles and their relation to Fractions

Hi friends, In today's article we all are going to discuss about a very important part of cbse syllabus that is angles/relate angles to fractions, Grade IV, geometry help. Before, we move to the topic, it necessary to know about what is angle?which can be used for your Homework help, An angle is defined as a shape, formed by two lines (line one is xy and other is yz and their meeting point is y) or rays diverging from a common point.
Now we are discussing about the Attributes and measurement of angles:- Attributes (Vertex, Legs, Interior, and Exterior) are nothing but the parts of an angle. From the study of these attributes it is easy to understand an angle.
Vertex: The common point at which the two lines or rays are joined is called vertex. If xy and yz are two lines then the vertex point is y and vertex of the angle is xyz.Get further details on fraction here,
Legs: Legs or sides of an angle are the two lines that make it up. From the above, the lines xy and yz are the legs of the angle xyz.
Interior: The interior of an angle is the space by which the angle extending out to infinity.
Exterior                : All the space on the plane that is not the interior is called exterior.
Measure of an angle:-In measurement of angle the size of an angle is measured in degrees .When we say the angle xyz we mean the actual angle object. If we want to talk about the size or measure of the angle in degrees we should say the measure of the angle xyz.
Let’s we discuss about the types of angle and these angles are used in mathematics, sciences even in real world problems etc. These angles are explained one by one in below:
Acute Angle: Acute Angle is an angle that is less than 90°.
Right Angle: Exact 90° angle is called right angle.
Obtuse Angle: Obtuse Angle is an angle that is greater than 90° but less than 180°.
Straight Angle: Exact 180° angle is called Straight Angle.
Reflex Angle: Reflex Angle is an angle that is greater than 180°.
Now we are taking some examples: - Let the values of angles a, b, c, d, e and f are 31⁰,
90.5⁰, 90⁰, 130⁰,37⁰,42.8⁰  respectively. Now from these values of angles the Acute Angles is a, e and f, Obtuse Angles is b and d, right angle is c. Like this we find all the angles.
Now I am telling you something about Pairs of Angles. Pairs of angles are created when parallel lines get crossed by another line which is called a Transversal. These pair of angles has special names and their names are vertical angles, corresponding angles, alternate interior angles, alternate exterior angles, consecutive interior angles.
Lastly I am telling you one more angle that is Angles around a point. Angles around a Point are a 360⁰ angle and made a circle. For example 53°, 80°, 142°, 85° are the values of angles. When we add these then the sum is 360⁰.
53°+ 80°+142°+ 85°=360⁰    
From the above discussion I hope it would be help you to understand Angles/relate angles to fractions, Grade IV, geometry and if anyone want to know about Factors and products then they can refer to internet and text books for understanding it more precisely.Read more maths topics of different grades such as Decimals and Place Values in the next session here.

Transformations using Concrete Models

Children,In last session we read about real numbers examples and Today we are going to give tutors on Geometry and their transformations using concrete models which falls under the syllabus of gujarat state education board . Today we will study about  point, line, line segment, ray, Plane, parallel lines and perpendicular lines.

POINT: A point in the space represents the exact location in the space. It is always represented by a dot(.) and it has no length or thickness. It is represented by Capital Alphabets of English. Here are some points.
     .A        .X      .N        .P
Here A, X, N,P represents the points. We must always use a sharpened pencil to draw various geometrical figures.
LINE:  When many group of points joined together , if drawn in same plane and direction forms a line. It extends endlessly in both direction and has no fixed length. It has no end points.
                             A <-------------------------->    B
Here AB represents a line and its arrows on both sides represents that it extends in both the directions. Example for line is the edge of endless straight road.

LINE SEGMENT: A line segment is the part of a line and it has a fixed length.  A line always has a starting and  end point. It is represented as  XY. Edge of a window , ruler or a table top represents a line segment.
                              X__________________________Y
HOW TO MEASURE A LINE SEGMENT:  As we know a line segment has a start and end point. We place the ruler mark “0” at the start of a line and then check the exact location of the end point of the line. It gives us the length of a line segment. (want to Learn more about transformations ,click here)

1. RAY: A ray is the portion of a line which has a starting point but no end point. It extends endlessly in only one direction. Ray of a torch or a sun beam represents a ray. It is represented as PQ. Ray PQ means its starting point is P and it extends in Q direction.

                                 
PLANE: The surface of any solid figure may be flat or curved. If the surface is flat then it is called Plane surface. Example of a flat surface is table top, wall , plain road etc.
                It the surface of the object is curved then it is called the curved surface. Example of the curved surface are ball, globe and sphere.
 PARALLEL LINES: The two lines are parallel to each other if they are at equal distance at all the points. It means that they do not meet. If we see the railway track or even the two opposite edges of a ruler, they are at equal distance at all the points , so they are parallel. ‘II’ sign represents the pair of parallel  
 In the above figure, we have AB II CD
                                               A________________________________B
                                               C________________________________ D
PERPENDICULAR LINES: A pair of lines are perpendicular , if one line makes angle of 90^o with another. An English Alphabet T is the example of perpendicular lines.  Here in the given figure Line segment AB is perpendicular to Line segment BC. Also line segment BC is perpendicular to line segment CD.

                                             A __________________|B
                                                                                |
                                                                                |
                                                                                |
                                                                                |C
                                                                                |____________________D


This is all about the geometry transformations  and if anyone want to know about Properties of odd/even numbers then they can refer to internet and text books for understanding it more precisely. You can also refer grade V blog for further reading on Mean and median in Maths.

Learn finding Area, Circumference and Perimeter

Hello Friends, in today's class we all are going to discuss about some of the most interesting topics of mathematics, geometry, area, circumference and perimeter which comprises of a huge part of cbse question bank. Here I am going to tell you the best way of understanding these terms.
Now start with basic geometry help:
Geometry is the basic about the point, lines, angle, area, volume etc. And to learn it we should have knowledge of some terms:

1.    Point:

Point is represented as a dot in a plane. Usually we denote it with a capital letter.

2.    Line:

Line is described as the collection of points. Line does not have any end point i.e. it extends forever.

3.    Line segment:

Line segment is a part of line that has two end points.

4.    Ray:

Ray is defined as the a line which starts from a point and extends in a direction forever in simple words we can say that line with a single end point.           

5.    Angle:

When two rays start from same point then they form an angle between them.                                  

                   

6.    Plane:

Plane can be defined as a flat surface that extends forever.                              

And now we will start learning about the terms area, circumference and perimeter. And remember one thing that all these terms have their own geometrical formulas for each and every figure i.e. formulas of area are different for circle, triangle, rectangle etc. and similarly this is also in the case of circumference and perimeter. Click here to know more about Geometry.                                  

Now one by one we will go through to each term and see their formulas for different shapes:

1.    Area:

Area is calculated in “square” units and the area of a given plane surface is equal to the number of squares required to cover it.

1.    Square: b²                                                   

2.    Rectangle: l x b => ( length x breath )

3.    Parallelogram: b x h => ( breath x height )

4.    Trapezoid: h ( b₁ + b₂ )

                  2

5.      Circle: pi r²   ( pi = 3.14)

6.      Ellipse: pi r₁² r₂²

7.    Triangle: ½ ( b x h )

8.    Equilateral triangle: sqrt ( 3 ) ( a² )

                                      4

         
             Let’s take an example:
            Q1. Find the area of a circle whose diameter is 4 cm. ( pi = 3.14 )
            Solution:
                        Diameter of a circle = 2r
                        Therefore     4 = 2r
                                             r = 2 cm
                        Area of a circle = pi r²
                                                                             = 3.14 x 2²
                                                 = 12.56 cm²

2.    Perimeter:

Perimeter is defined as the sum of all sides of a figure.

1.    Square: 4b 

2.    Rectangle:2p + 2q 

3.    Triangle:p + q + r   

4.    Circle: 2pi r  

5.    Circle:  pi d (where d is the diameter)

           Let’s take an example:
            Q1. Find the perimeter of a square whose edge length is 4 cm.
            Solution:
                        Perimeter of a square = 4 x (edge length)
                                                            = 4 x 4
                                                            = 16 cm

3.    Circumference:

Circumference is defined as the distance around any closed surface.

1.    Circle: 2 pi r

               Let’s take an example:
            Q1. Find the circumference of a circle whose radius is 4 cm. ( pi = 3.14 )
            Solution:
                        Circumference of a circle = 2 pi r
                                                                 = 2 x 3.14 x 4
                                                                 = 25.12 cm

This is all about the finding Area, Circumference and Perimeter and if still it is not clear to anyone they can refer to internet and text books for understanding it more precisely. You can also refer grade V blog for further reading on geometry. You can read more maths topics of different grades such as Numbers in Grade IV on Internet.

 
         

Geometric Figures in Grade IV

Hello friend’s,today I am going to discuss the important topic for grade IV of karnataka education board which are geometry,geometry help, geometric figures, attributes. So today we will start the brief discussed about that topic.
Let’s start with definition of Geometry. You know friend, geometry is very important set of topic for math students. By geometry we can make a line, triangle, circle, angle etc.  These are the applications of the geometry. By geometry we can solve very big problems in short way.
Let’s start with line what is line in geometry? In geometry line has three properties.
Line is straight (no curve),
Line has no thickness
Line can be extended in both directions without end.


Various types of lines:includes Straight line, Parallel lines, Perpendicular line.
Let‘s discuss the another shape:
Quadrilaterals:  Quadrilaterals are like a shape which has four sides. Given below are some quadratics with figure:
. Rectangle

.Parallelograms

.Rhombus

.Square

.trapezium


Let’s move on other shape:(To know more about geometrical figures click here)
Circle: A circle is like a closed loop which has a fixed distance from the center point.
Properties of a circle:
Center: a point inside the circle and all points on the circle have same distance from the center point.
Radius: the radius is distance from the circle point and also it’s half of diameter.
Diameter:  this is twice of the radius.
Circumference: this is distance all around the circle.
Tangent: a line that is touching the circle at just one point.
Secant: A line that intersect a circle at two points that is secant.
Let’s move on other application:
Triangle: triangle has three sides and three angles.
It’s also called 3-sided polygon.

Triangle properties:
Vertex: vertex is a corner of the triangle and every triangle has three vertices.
Base: any triangle of the bottom side is called base this depends upon area of triangle.
Altitude: altitude of a triangle is the perpendicular from the base to opposite vertex.
Median: when three lines intersects at single point it is called median. This also called cancroids of the triangle.
Interior angles:  the three angles on the inside of the triangle at each vertex which angle is called interior angle. (In a triangle the shortest side is always opposite the smallest interior angle.)
Exterior angle: In a triangle, the angle between triangle and the extension of an adjacent side which is called exterior angles. (In a triangle the longest side is always opposite to the largest interior angle.)

Types of triangle:  there are seven types of triangles and these have own properties.
Isosceles:    in this triangle two sides are equal
Equilateral: in this triangle all sides are equal.
Scalene:  in this triangle no sides are equal.
Right triangle:  in this only one angle is 90⁰
Obtuse: in this triangle only one angle is greater than 90⁰
Acute: in this triangle all angles less than 90⁰.
Equiangular:  in this triangle all interior angles are equal.

So friends that was the basics of the geometry. We hope you have understood the topics very well. To know about grade V topics and Parallel lines, perpendicular lines, geometry wait till next session.