Question

ABC is a triangle in which right angled at B prove that a b square is equal to BC square​

Answer 1

ΔABE is a right triangle, right angled at B

AB²+BE² = AE²……………..(1)

(by the Pythagoras theorem)

ΔDBC is a right triangle, right angled at B

DB²+BC² = CD²…………….(2)

(by the Pythagoras theorem

Adding eq 1 & 2

AE²+CD²= (AB²+BE²)+(BD²+BC²)

AE²+CD²= (AB²+BC²)+(BE²+BD²)......(3)

[Rearranging the terms]

ΔABC is a right triangle,

AB²+BC² = AC²…………….(4)

(by the Pythagoras theorem)

Δ DBE is a right triangle

DB²+BE² = DE²………………(5)

(by the Pythagoras theorem)

AE²+CD²= (AB²+BC²)+(BE²+BD²)

AE²+CD²= AC²+DE²

[ From equation 4 and 5]