D and E are points on the sides CA and CB respectively of a triangle A

1.	D and E are points on the sides CA and CB respectively of a triangle ABC right angled at C. Prove that AE2 + BD2 = AB2 + DE2 .
Answer» Data: In ∆ABC, ∠C = 90°, D and E are points on the sides CA and CB respectively To Prove: AE² + BD² = AB² + DE² In ⊥∆ACE, ∠C = 90° ∴ AE² = AC² + CE² ………. (i) In ⊥∆DEB, ∠C = 90° ∴ BD² = DC² + CB² ………… (ii) From adding equations (i) + (ii) AE² + BD² = AC² + CE² + DC² + CB² = AC² + CB² + DC² + CE² ∴ AE² + BD² = AB² + DE² (Theorem 8).

D and E are points on the sides CA and CB respectively of a triangle ABC right angled at C. Prove that AE2 + BD2 = AB2 + DE2 .

Answer»

Data: In ∆ABC, ∠C = 90°, D and E are points on the sides CA and CB respectively

To Prove: AE² + BD² = AB² + DE²

In ⊥∆ACE, ∠C = 90°

∴ AE² = AC² + CE² ………. (i)

In ⊥∆DEB, ∠C = 90°

∴ BD² = DC² + CB² ………… (ii)

From adding equations (i) + (ii)

AE² + BD² = AC² + CE² + DC² + CB²

= AC² + CB² + DC² + CE²

∴ AE² + BD² = AB² + DE² (Theorem 8).