Congruence in Grade VII

Hello friends, in grade VI we get basic idea and geometry help according to grade VI, but in grade VII of Gujarat Board Syllabus we will  have to learn new concept of geometry and learn solving equations based on it. So, in today's session we all are going to discuss about one of the most interesting topic of geometry which is congruence.
Two objects are said to be congruent, if one object is the exact copy of another object means both objects have same shape and shape size like two  photocopied papers are called as a Congruent because both have same size and same shape and relation of two objects being congruent is  called a congruence. So, first of all we will discuss concept of congruence  :
Congruence of plane figures: if one plane figure matches with another figure then this relation is called as Congruence between plane figures  like

if we put one figure onto another figure, it completely covers the other and when two figures completely covers each other then relation between these two plane figures are called as a Congruence of plane figures.(want to Learn more about Congruence,click here),
Congruence between lines: If two lines are equal means both lines have same length then both lines are called as a congruent lines. For understanding congruence between lines, we take two lines AB and CD

if we put CD on AB and it covers AB completely means C covers A and D covers B then CD and AB called as a congruent and relationship  between these two lines are called as a congruence between these two lines.
Congruence of angles: when angle between two line segments are same then this relationship between two angles is called as a congruence of  angles. For understanding congruence of angles, we take an example

here both angles A and B are same. These two angles are known as congruent angles.
Congruence of triangles: There are some rules which define Congruence of triangles

• side-angle-side rule : when two sides and one angle of triangle is equal to another triangle then both triangles are known as a congruent triangles. like. The figure below shows this.

Here two sides are 4cm and 5cm and one angle 100 degree are equal to other triangle. So both triangles are known as a congruent triangles.

• angle-side-angle rule : when two angles and one side of triangle is equal to other triangle then both triangles are known as a congruent  triangles as shown in the image below

       
here two angles 75 degree and 65 degree and one side 10cm are equal to other triangle, then both triangles are known as congruent triangles.

• side-side-side rule : if all three side of one triangle is equal to all side of other triangle then both triangles are said to be congruent  triangles as shown in the image below

Here all three sides are equal to each that's why both triangles are known as a congruent triangles.

• angle-angle-angle rule: if all angles of one triangle is equal to all angles of other triangle then both triangles are said to be congruent triangles.

Here all angles are same in both triangles so both triangles are known as congruent triangles.
This is all about rules to prove congruence between triangles and if anyone want to know about Eighth grade quadratic equations then they can refer to Internet and text books for understanding it more precisely. You can also refer Grade VII blog for further reading on Measurements in Mathematical World.
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Tessellations in Grade VII

Previously we have discussed about list of rational numbers and In today's session we are going to discuss about Tessellations which belongs to grade VII of maharashtra state education board. Generally in mathematics you didn't heard this term but it has a relation with mathematics. A tessellation is a pattern made by repeating shapes. Making Tessellations require a creativity of an art with capability of solving puzzles. In this world there are many natural tessellations also present.

In modern world very few people are aware of the term Tessellations. The connection between math and art is very strong and frequent but very few people are aware of that. Tessellation also covers a regular space without overlapping and without leaving any space. For example a chessboard is a Tessellation, made of squares with no gap in between and without overlapping. The pattern of the brick on a wall is a Tessellation. made by rectangle.

Now let’s see how we can solve math problems for free related to Tessellations,

Now we have a task that  we want a cover a floor with tiles. We can cover it with square tiles since square tiles never leave gaps and always fit together. But in this activity we will try it with a rectangle where we will provide some very good shapes to that and then make a Tessellation by repeating its shape over and over again. It is a very interesting thing to do.

We require following things for making this Tessellation.

Ruler

Pencil

Scissors

Index card 3” *5”

Transparent tape

Colored marker and pen

2.5” *3” grid paper

Now we need to follow the steps below

Cut the index card in half and create rectangle

Fix the area of the rectangle (area=length * breadth)

Now draw a line between two adjacent corners on one of the longer side of a rectangle. Your line must be straight.(want to Learn more about ,click here),

Cut along the line you draw. Now take the piece you cut outside and slight it across the opposite side of the triangle.

Now you find a new shape that you never seen before. Now you just need to take this piece out and now draw another line that connects two adjacent corners on one of the short size of the shapes.

Now you need to cut it along new line and you will get a shape which is little smaller than the previous one. Take the piece out and now combine all the pieces, now you can see you made a Tessellation.  

Now let’s move to four color theorem. According to this theorem if we have a Tessellation of four colors in such a manner that no same color is together in such a manner no tiles of same color meet at the curve of positive length.

If we talk about intuitive statement of four color theorem that any given separation of the plane in to contiguous regions called as map, the region can get colored using most four color such that no two adjacent regions have the same color.

Note: each region of the map should be contiguous otherwise we add new demand to the statement, which the theorem doesn’t have.

If we talk about real world, not all countries are contiguous. Countries like Russia, USA, Alaska are not contiguous because the  territory of particular country must be of same color. Four colors are not sufficient

This is all about tessellations and if anyone want to know about Representing probability

then they can refer to internet and text books for understanding it more precisely .Read more maths topics of different grades such as Pythagorean theorem  in the next session here.

Learn properties of 2-d and 3-d figures in mathematics

Friends,Previously we have discussed about rational numbers examples and today i am going to teach you the properties of 2-d, properties of 3-d which are the most interesting and unique topics of mathematics and generally studied in grade VII of tamilnadu education board. Here I am going to tell you the best way of how to solve math problems related to it.

The dimension can be defined as the minimum number of coordinates are used to specify a point in any shape or object. Therefore line is a one dimension shape because only one coordinate is required to specify a point in it. A rectangle is lies in a place or a surface has two dimensions because two coordinates are needed to specify a point in it and hence it has both length and breath. The cube has three dimensions because three coordinates are needed to specify a point in it and hence it has length, breath and depth.(Learn more about area of 2-d figures by clicking here)

Let's see some properties of 2-d and 3-d shapes with there examples:

1. 2-d figures:

2-Dimension figures or shapes can be defined in the terms of length and breath or you can say length and height. 2d figures or shapes do not have their volume and depth.

Properties of 2-d figures:

1. 1. 2-d figures can only be expressed in terms of length and breath.
   2. We can't find the volume of 2-d figures.
   3. We can't assume the depth of 2-d figures.
   4. 2-d figures are flat and can be easily figure out on a paper.
   5. 2-d figures can also be called as plane figures.

Examples of 2-d figures:

1. 1. 1. Square: A 2-d figure with four edges equal to each other and opposite sides are parallel to each other and also have 4 interior angles.
      2. Rectangle: A 2-d figure with four edges and opposite sides are parallel to each other and also have 4 interior angles.
      3. Pentagon: A 2-d figure with five edges and also have 5 interior angles.
      4. Parallelogram: A 2-d figure with four edges and opposite sides are parallel to each other.
      5. Triangle: A 2-d figure with 3 edges and also have 3 interior angles.
      6. Octagon: A 2-d figure with 8 edges and opposite sides are parallel to each other and also have 8 interior angles.
      7. Hexagon: A 2-d figure with six edges and opposite sides are pallel to each other and also have 6 interior angles.

1. 1. 2. 3-d figures:

3-Dimension figures or shapes can be defined in the terms of length, breath and depth. 3d figures or shapes have their volume and depth.



Properties of 3-d figures:

1. 1. 3-d figures can be expressed in terms of length,breath and depth.
   2. We can find the volume of 3-d figures.
   3. We can assume the depth of 3-d figures.
   4. 3-d figures can be solid or hollow.

Examples of 3-d figures:

1. 1. 1. Cube: 3-d figure with six faces equal to each otherin size.
      2. Hemisphere: 3-d figure equal to half of sphere.
      3. Cuboid: 3-d figure with six rectangular faces.
      4. Cylinder: 3-d figure with circles on each end.
      5. Cone: 3-d figure with circle at the base and vertex on the top.
      6. Sphere: 3-d figure with perfectly round shape and has only one curved face.
      7. Pyramid: 3-d figure with polygon at the base and triangle faces all around it.                                                                                                                                                                                                                                                          

This is all about Properties of 2-d figures and 3-d figures of Grade VII and if anyone want to know about Tessellations and also about Sampling techniques then refer to Internet.

Understand Regular and Irregular Shapes in Geometry

Hello Friends, Earlier we have discussed about analytic geometry problems and in today's session we all are going to discuss about some of the most interesting topics of mathematics regular and irregular geometric shapes which are usually studied in Grade VII of tamilnadu education board. Here I am going to tell you the best way of understanding these topics.
Now start with basics about geometry and you can refer Internet for further geometry help:
Geometry is the basic about the point, lines, angle, area, volume etc and to learn it we should keep some points in our mind like a point is represented as a dot in a plane, a line is described as the collection of points, a line does not have any end point, a line segment is a part of line that has two end points, a ray is defined as a line which starts from a point and extends in a direction forever, when two rays start from same point then they form an angle between them, plane can be defined as a flat surface that extends forever.
Now we start with the regular geometric shapes. Regular geometric shapes are those which have predefined dimensions and predefined angles.There are many regular geometric shapes which are as follows:(Learn more about geometry here),

1.    Triangle: A polygon having three sides and sum of the angles is 180 degrees.

2.    Equilateral triangle: A triangle with sides equal in length and all angles are 60 degrees.

3.    Right triangle: An angle measures 90 degrees.

4.    Quadrilateral: A polygon with four sides and sum of the angles is 360 degrees.

5.    Rectangle: A polygon with four sides with all right angles

6.    Square: A polygon with four sides with equal sides and intersects each other at right angles.

7.    Parallelogram: A polygon with four sides with two pairs of parallel sides.

8.    Rhombus:A polygon with four sides with all equal sides and sum of the angles is 360 degrees.

9.    Trapezoid: A polygon with four sides with one pair of parallel sides. The parallel sides are known as the bases of the trapezoid and sum of the angles is 360 degrees.

10. Pentagon: A polygon with five sides and sum of the angles is 540 degrees.

11. Hexagon: A polygon with six sides and sum of the angles is 720 degrees.

12. Circle: A circle is the collection of points in 2D plane having equal distance from a fixed point known center and a line segment joining the center to any point on the circle is known as radius.

There are many more regular geometric shapes like Isosceles triangle, scalene triangle, acute triangle, obtuse triangle, heptagon, octagon, nonagon, decagon, convex.
Now move to the irregular geometric shapes. Irregular geometric shapes are those which do not have predefined dimensions and angles and are constructed using different regular geometric shapes. To calculate area of irregular geometric shapes, the first thing to do is break the irregular shape into regular shapes that can be identified individually as triangles, rectangles, circles, squares etc.
From the above discussion we can understand the basics about the regular and irregular geometric shapes and if anybody needs more about these Geometric concepts they can refer to internet and their text books.Read more maths topics of different grades such as Graph and Slope of Lines in Grade VIII in the next session here.