First, we construct a right angle triangle right angle at B

Now, construct  a perpendicular BD on side AC.

Now, ∠B = 90 degree

Now, in Δ ABD and Δ ABC

∠A = ∠A

∠ADB = ∠BDC = 90 degree

So, Δ ABD is similar to Δ ABC

=> AD/AB = AB/AC    {sides are proportion}

=> AB² = AD * AC  ...........1

Similarly, we can show that Δ BDC is similar to Δ ABC

=> BC/DC = AB/BC    {sides are proportion}

=> BC² = AC * DC  ...........2

Now, add equation 1 and 2, we get

=> AB² + BC² = AD * AC + AC * DC

=> AB² + BC² = AC(AD + DC)

=> AB² + BC² = AC * AC

=> AB² + BC² = AC²

Hence, in a right traingle, the sqaure of the hypotenuse is equal to the sum of the squares of the other two sides.