Question

State pythagoras theorem class 10

Answer 1

See the attachment...

Answer 2

.Pythagoras Theorem

Statement: In a right angled triangle, the square of the hypotenuse is equal to the sum of squares of the other two sides.

Given: A right triangle ABC right angled at B.

To prove: AC2 = AB2 + BC2

Construction: Draw BD perpendicular toAC



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.

triaADB and triABC

So, (Sides are proportional)

Or, AD.AC = AB2 ... (1)

Also, triBDCand triABC

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
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Hence Proved.