Learn Pythagorean Theorem

Hello friends today we are going to learn about Pythagorean Theorem also known as Pythagoras Theorem

Pythagorean Theorem Examples: This theorm was derived by a greek mathatician Pythagoras .It is related to all sides of a Triangle and can be applied to those triangle who is having one 90 degree angle.• Arms (a and b): the sides of the triangle adjacent to the right angle. They should not be of same length to apply Pythagorean theorem
• Hypotenuse (c): the side of the triangle opposite the right angle
Theorm :
Equation :Equation :a²   +   b²    = c²

The sum of the squares of the two sides is equal to the square of the hypotenuse


 Lets take an acute angle triangle abc here angle a and b are acute angles a and b angles are acute angles less than 90 degree and one angle i.e c is of 90 degree to give a sum of 180 degrees.In this angle there is no obtuse angle (angle greater than 90 degree)to apply the theorm
This theorm is very useful for finding the any side of a right angle triangle . If the length of any side is not known it can be calculated by using
Where a and b represents length of other two sides and c represents length of the hypotenuse ,the longest side
Pythagorean theorem help with more Examples. (visit for detail)
Example 1: Prove a triangle with sides “2, 3 , 4” is having a 90 degree angle in it
Solution = 2*2+3*3 =4*4

Example2 :Find the side of the Triangle(12,5  , c) ?
In this question values and info we are already having are two side length and one angle is of 90 degree.So to calculate the length of the third side we can apply the Pythagorean theory
A² +b ²=c²
12*12+5*5=c²
144+25=c²
169=c²
13=c

This theorm will be helpful to everyone till grade XII

In upcoming posts we will discuss about Congruence and Applications of Probability and Statistics. Visit our website for information on Karnataka state board books

Conditional statements

Hi Friends! In this session of solve math problems we will discuss about conditional statements. Conditional statements are the statements that check the true and false value for every given statements. In Conditional statements some statements shows that they are universally true (like:-sun rises from east) and some are false. In free online math tutoring sessions Conditional statements are generally same in every grade either grade XII or others. These statements are used in computer science in programming languages.
Conditional statements are:-
-If then else conditional statements are used to execute if block when this is true if it is not true than it goes to the else block and execute it syntax for it:-
if(condition)
statement1;
else if(condition2)
statement2;
-Else if is the nested if else block that have multiple else blocks.
if(condition1)
statement1;
else if(condition2)
statement2;
else if(condition3)
statement3;
else
statement-n;
-Switch statements are also used to check multi way conditional statements.
switch(expression)
case choice1:
statement1;
case choice2:
statement2;
case choice-n:
statement-n;
-Conditional operator (?) is also used to check true or false value for given statements syntax for this is:-
Condition ? Expression 1 for condition true : Expression 2 for condition false
Many operators are used to check statements like :-
logical operator:- AND, OR, NOT, XOR.
Comparison operator:- =, <=, >=, !=.
Conditional statements examples can be understand by converse, inverse and contra positive expressions.
If the deer will run then tiger will hunt the deer---conditional.
If the deer won't then the tiger won't hunt the deer---inverse.
If the tiger will hunt the deer then the deer will run---converse.
It the tiger won't hunt the deer then the deer won't run---contra positive.
If p then q conditional
if q then p converse
if p will be negation than negation q inverse
if negation q then negation p contra positive
Logically equivalent will be conditional expression and its contra positive.

In upcoming posts we will discuss about Geometric proofs in Grade XII and Correlation coefficient. Visit our website for information on school education Karnataka