Pythagorean theorem

Previously we have discussed about calculate the volume of a sphere where the radius is 9 meters. and In today's session we are going to discuss about Pythagorean theorem which comes under school of secondary education andhra pradesh, Pythagorean Theorem was given by the ‘Pythagoras’ a Greek mathematician. Pythagorean Theorem can be defined as the square of a hypotenuse is equal to the sum of the square of the base and square of the perpendicular that is the opposite side of the hypotenuse in a right angled triangle. If we define it in the form of expression then it will be denoted as,
(Hypotenuse) ² = (base) ² + (perpendicular) ².
For Example: A Right angled triangle named as XYZ and if ‘Z’ is a hypotenuse of right angled triangle and ‘Y’ is base and ‘X’ denotes the perpendicular then Pythagorean theorem can be expressed as (Z) ² = ( X) ²+ (Y) ² .
We can explain it by taking an example as;
If the base = 12 inch (Y = 12 inch) and perpendicular = 5 inch (X = 3 inch) then find the length of hypotenuse ‘Z’ in meters by using the Pythagorean Theorem?
Solution: Pythagorean Theorem proof
(Hypotenuse) ² = (base) ² + (perpendicular) ²,
Then (Z) ² = (X) ² + (Y) ²,
(Z) ² = (12) ² + (5)²,
Z = √ (12) ² + (5)²,
Z = √ (144) + (25),
Z = √ 169,
Z = 13 inch.
So according to the calculation, the length of the hypotenuse in a right angled triangle XYZ is 13 inch.
Pythagorean Theorem is used in the case when two sides of the right triangle are given and for calculating the third side of the tight angled triangle, we are use the Pythagorean Theorem.
In the next session we are going to discuss Grade VII, Rectangular coordinate system and You can visit our website for getting information about algebra help online.

Congruence

Previously we have discussed about tangent line approximation and In today's session we are going to discuss about Congruence which is a part of school boards in india , In geometry if we are given two figures and the question is asked that are the two geometrical figures congruent, for this we need to recall the congruence definition. According to Congruence, two or more given geometrical figures are congruent if they have all the sides of the equal measurement and the angles formed by all the line segments are exactly equal. We say the two figures are congruent, if the two figures are placed one over another, they overlap each other.
Let us first take two circles, the two circles are said to be congruent, if they are drawn with the same radius.
 In case of the square, we say that the two squares are congruent, if they are formed with the help of the same line segment. As we know that all the angles of squares are equal to 90 degrees each, so we say that the two squares are congruent if they have the length of each side of the same measure.
Now we take the two rectangles, the two rectangles are said to be congruent, if the length of one rectangle is equal to the length of another rectangle and the breadth of one rectangle is equal to the breadth of another rectangle. All the rectangles have all the angles equal to 90 degrees. If we place one rectangle over another, the two rectangles are found to be exactly of the same measure and they overlap each other.
 In case of the triangles, we know that the triangles are formed by joining 3 line segments. Here we say that the two triangles are congruent, if the three sides of the lines are congruent   and the corresponding sides of the triangle are also equal, then the triangles are said to be congruent.
 In the next session we are going to discuss Basic constructions and You can visit our website for getting information about chemistry answers.

Congruence in Grade VII

Hello students today we are going to discuss Congruence. In mathematics you have to deal with many topics, congruence is one of them. If there are two or more objects or figures that have the same size and same shape, they are called congruent objects or figures. In other words the figures are called isometric, i.e. they have same size and same shape. In congruence we can reposition the objects in other shapes than they known as translation, rotation and reflection and combination of all called is transformation. Let’s take an example of triangle that will surely help you to understand this:-If      Two triangles have same corresponding size and same corresponding shape than they are congruent. As shown in figure we have two triangles ABC and DEF and in first triangle AC=7, CB=6 and in second triangle DF=7, FE=6. This implies both the triangles have same size and same shape so we can show their relationship in this way:-

∆ABC≅∆DEF

To determine congruence we have some comparisons, they are:-

-Angle side angle.

-Angle angle side.

-Side angle side.

-Side side side.

-Right angle hypotenuse side.

If any one of the comparisons exists in any figure than they are said to be congruent figures. Generally congruence may be defined in many fields like:-

-In relation.

-In modular arithmetic.

-In groups and subgroups.

-In number theory.

-In general relativity.

-In graphs.

And congruence is present in those shapes where equality is there; like in figures, objects, relations, groups and in many fields.

 

The above described congruence information will surely helpful for grade VII students. In the next topic we are going to discuss Relation between objects in space.

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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