ABC is a right triangle. right angled at A and D is the midpoint of AB. Prove that BC²=CD²+3BD².
Answers
Answered by
5
Answer:
In triangle ABC
By pythagoras theorem
BC2=AB2+AC2....(1)
In triangle ADC
CD2=AC2+AD2
AC2=CD2-AD2
from (1)
BC2=AB2+CD2-AD2
BC2=(AD+BD)2+CD2-AD2
BC2=AD2+2AD.BD+BD2+CD2-AD2
BC2=2AD.BD+BD2+CD2
since D is a midpoint of AB
AD=BD
BC2=2BD2+BD2+CD2
BC2=3BD2+CD2
Similar questions