Pythagoras theorem Class 10 (also called Pythagorean Theorem) :
it states that : “In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides“.
Note: Here the sides of this triangle are named as Base, Perpendicular and Hypotenuse.
Here, the hypotenuse is the longest side, opposite to the angle 90⁰.
Given: A right triangle ABC in which B is right angle.
To Prove: AC² = AB² + BC²Construction: Draw a perpendicular line BD, which meets AC at D.
Proof:
By Theorem 6.7: If a perpendicular is drawn from the vertex of the right angle of the a right triangle to the hypotenuse then the triangle on both sides of the perpendicular are similar to the whole triangle and to each other.
So, △ADB ~ △ABC,
Therefore,
⇒ 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 theorem is proved.