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.

Basic constructions

Hello students, Previously we have discussed about who invented calculus and in this blog we are going to discuss basic constructions which comes under andhra pradesh education board. In basic construction generally we include the construction of similar triangles, tangents to circles and the basic constructions in geometry which include: -
-Construction of various angles such as 30°, 45°, 60°, 90^o.
-Bisecting an angle.
-Constructing a line parallel to a given line through a given point.
-Construction of perpendicular bisector of a line.
-Construction of closed figures like squares, rectangles, quadrilaterals etc.
-Construction of in circle, circum circle and ex circle of a given triangle.
All of the above construction uses compass and ruler.
If we talk about more simple geometry then basic construction include: -
-Constructing of line (basic construction in geometry).
-Constructing of triangle.
-Construction of circle.
Let’s take one construction from the above list to see the basic construction in geometry.
Construction of triangle: - Triangle is a three sided close figure. Triangle can be constructed using the ruler, compass and protractor.
Some steps to construct the triangle are: -
Step 1: - A triangle has three side then XY = a units YZ = b units and ZA = c.
Step 2: - Draw the line XY = a units using ruler.
Step 3: - Take a compass and measure c units with the help of ruler.
Step 4: - With X as center, cut an arc above the line segment XY with the help of compass.
Step 5: - Again take a compass and measure b units.
Step 6: - With Y as center cut an arc above the line segment XY.
Step 7: - Both the arcs meet at a point that is Z.
Step 8: - Join XZ and YZ. Now, XYZ is the required triangle.

In the next session we are going to discuss Grade VII, Pythagorean theorem and You can visit our website for getting biology help.

Pythagorean Theorem in Grade VII

In Euclidean Geometry, Pythagorean theorem is given for three sides of right triangle. Right triangle is described as a triangle whose one angle is a right angle i.e. 90'. Pythagorean theorem states that square of the side opposite to the right angle known as hypotenuse is equal to the sum of the square of other two sides of the right triangle. We can define it by an equation known as the Pythagorean Theorem Worksheet as:
If a right triangle have three sides a , b and c then according to the Pythagorean theorem of maths the relation between the sides is A² + B² = C² where C is a hypotenuse of right triangle and A and B are two other sides of right triangle .
If the two sides of the right triangle are given then we can calculate other third side by using the Pythagorean theorem.  (To get help on cbse syllabus click here)
Let us assume that A side has the length of 3 centimeters and side B has the length of 4 centimeters then the length of the hypontenuse is A² + B² = C²

So according to the Pythagorean theorem, length of c is 3² + 4² = c² . By solving this equation we get the value of C is 5 as C = ( 3² + 4² )^½
= ( 9 + 16 )^1/2 = ( 25 )^1/2
= 5 centimeters.
Example: If we have the length of hypotenuse as 13 centimeter and one of its side is 5 centimeter then calculate the length of other remaining side.
Solution: We are given that A=5, C=13. We have to find B.
5² + B² = 13² then value of B as B² = 13² – 5² then
B² = 169 – 25
B = ( 144 )^1/2
B = 12 centimeters
So In the next topic we are going to discuss Congruence and In the next session we will discuss about Congruence in Grade VII.