Question

Ad is median of triangle abc.Prove that,ab2 + ac2=2(ad2+bd2)

Answer 1

1. Question⇒   Ad is median of triangle abc.Prove that,ab2 + ac2=2(ad2+bd2)?

Step-by-step explanation:

• In ABC, if AD is the median, then show that AB2 + AC2 = 2[AD2 + BD2].  
• Given: AD is a median in ABC.
• To prove: AB2 + AC2 = 2[AD2 + BD2]
• Construction: Draw AE  BC  
• Proof:
• In right triangles AEB and AEC, using Pythagoras theorem
• AB2 + AC2 = BE2 + AE2 + EC2 + AE2 = 2AE2 + (BD - ED)2 + (ED + DC)2  
• = 2AE2 + 2ED2 + BD2 + DC2
• AB2 + AC2 = 2AE2 + 2ED2 + 2BD2 [since BD = DC]  
• = 2 (AE2 + ED2 + BD2)  
• = 2 (AD2 + BD2)  
• [Using Pythagoras theorem in AED]