10. ABC is a right triangle right-angled at B. Let D and E be any poin

1.	10. ABC is a right triangle right-angled at B. Let D and E be any points on AB and BCrespectively, Prove that A CD2 - Ac2+ DE2
Answer» 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

10. ABC is a right triangle right-angled at B. Let D and E be any points on AB and BCrespectively, Prove that A CD2 - Ac2+ DE2

Answer»

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