Question

ABC is a right angled triangle at B. D and E are any points on AB and AC respectively. Prove that AE² + CD²= AC²+ DE².

Answer 1

Answer:

are you sure that your question is correct

you can solve this problem if the points are on AN and BC not AB and AC

Answer 2

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]

[FIGURE IS THE ATTACHMENT hope this answer helped u