Question

state and prove the pyetha gerous theo​

Answer 1

Answer:

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°

Step-by-step explanation:

Proof :

We know that: If a perpendicular is drawn from the vertex of the right angle of a right triangle to the hypotenuse, then triangles on both sides of the perpendicular are similar to the whole triangle and to each other.

ADB ABC

So, (Sides are proportional)

Or, AD.AC = AB2 ... (1)

Also, BDC ABC

So,

Or, CD. AC = BC2 ... (2)

Adding (1) and (2),

AD. AC + CD. AC = AB2 + BC2

AC (AD + CD) = AB2 + BC2

AC.AC = AB2 + BC2

AC2 = AB2 + BC2

Hence Proved.

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