Question

. In AABC, D is the midpoint of side AB. Line DE |
side BC. A-E-C. Prove that point E is the
midpoint of side AC.​

Answer 1

we are given that ABC be a triangle and D be he mid point of AB and DE||BC  

so, AD  =  DB  ...(1)

so, in triangle, ABC&ADE

∠BAC=∠DAE          ...(common angle)

as  DE||BC  

so,  ∠ADE=∠ABC

and  ∠AED=∠ACB

so,  tri(ADE)∼tri(ABC)

AD/DB = AE/EC

from (1)

AE/EC = 1

=> AE = EC

SO, AC  =  AE+EC=2AE

=>  AE  =  (AC)/2