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Pythagoras Theorem
The other two sides here are the perpendicular and base of the triangle. Therefore, in a right triangle, the hypotenuse becomes its longest side, because they are opposite the 90° angle.
PYTHAGOREAN THEOREM का FORMULA
In a right triangle,
A is perpendicular
B is the base
C is the hypotenuse
Therefore, according to the definition of the Pythagorean Theorem, the formula would be:
Hypotenuse²= Perpendicular² + Base²
In other words, it would be:
C²= A²+ B²
Pythagorean theorem PROOF :
In a right triangle, the base and perpendicular make an angle of 90 degrees with each other. Therefore, according to the Pythagorean theorem, “The square of the hypotenuse is equal to the sum of the square of the base and the square of the perpendicular.”
“the square of the hypotenuse is equal to the sum of a base square and perpendicular square.”
To prove this theorem,
Let us assume a triangle ABC, at right angle to angle B.
We have to prove: AC²= AB² + BC²
To explain: We draw a straight line BD which meets AC at D.
Proof:
We know by the theorem that if a right angle is drawn from the hypotenuse of a triangle at right angle, then the two triangles on both sides of the perpendicular are similar to each other.
so,
△ADB ~ △ABC
Hence,
AD/AB = AB/AC (Condition for similarity)
Or, AB2 = AD × AC (1)
Also, △BDC ~△ABC (By applying the same theorem)
Therefore,
CD/BC = BC/AC (Condition for similarity)
Or,
BC2= CD × AC (2)
Now,
By 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 theorem is proved.
APPLICATIONS OF PYTHAGOREAN THEOREM
Some Applications of Pythagoras Theorem
- How to know if a triangle is a right triangle or not
- to find the diagonal of a square
- In a right triangle, we can calculate the length of any side if we know the lengths of the other two sides.
Number Series Questions for Bank Exams
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