Pythagorus triplet formula means?
Answers
hi mate,
Basically, the converse of the Pythagoras theorem is used to find whether the measurements of a given triangle belong to the right triangle or not. If we come to know that the given sides belong to a right-angled triangle, it helps in the construction of such a triangle. Using the concept of the converse of Pythagoras theorem, one can determine if the given three sides form a Pythagorean triplet.
Pythagoras Theorem Statement
Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“. The sides of this triangles have been named as Perpendicular, Base and Hypotenuse. Here, the hypotenuse is the longest side, as it is opposite to the angle 90°. The sides of a right triangle (say x, y and z) which has positive integer values, when squared are put into an equation, also called a Pythagorean triple.
Pythagoras Theorem Proof
Given: A right-angled triangle ABC.
To Prove- AC² = AB² + BC²
Proof: First, we have to drop a perpendicular BD onto the side AC
We know, △ADB ~ △ABC
Therefore,
AD AB
----- = -----
AB AC
(Condition for similarity)
Or, AB² = AD × AC …………………..……..(1)
Also, △BDC ~△ABC
Therefore,
CD BC
----- = -----
BC AC
(Condition for similarity)
Or, BC²= CD × AC …………………………..(2)
Adding the equations (1) and (2) we get,
AB² + BC² = AD × AC + CD × AC
AB² + BC² = AC (AD + CD)
Since, AD + CD = AC
Therefore, AC² = AB² + BC²
Hence, the Pythagorean thoerem is proved.
According to the definition, the Pythagoras Theorem formula is given as:
Hypotenuse² = Perpendicular²+ Base²
c² = a² + b²
The side opposite to the right angle (90°) is the longest side (known as Hypotenuse) because the side opposite to the greatest angle is the longest.
Consider three squares of sides a,b,c mounted on the three sides of a triangle having the same sides as shown.
By Pythagoras Theorem –
Area of square A + Area of square B = Area of square C
