Question

In the figure. given below, AD ⊥ BC. prove that c²= a²+b²-2ax​

Answer 1

Answer:

Pythagoras theorem states that in a right-angled triangle, the square on the hypotenuse is equal to the sum of the squares on the remaining two sides.

First, we consider the ΔABD and applying Pythagoras theorem we get,

AB2 = AD2 + BD2

c2 = h2 + ( a - x )2

h2 = c2 - ( a - x )2 ......(i)

First, we consider the ΔACD and applying Pythagoras theorem we get,

AC2 = AD2 + CD2

b2 = h2 + x2

h2 = b2 - x2 ......(ii)

From (i) and (ii) we get,

c2 - ( a - x )2 = b2 - x2

c2 - a2 - x2 + 2ax = b2 - x2

c2 = a2 + b2 - 2ax

Hence Proved.