Question

show that the straight line joining the midpoint of two sides of a triangle is equal to half the third side​

Answer 1

Answer:

Draw a // line CG to BE

and join FG

now in triangle AEF and CGF

1) 1/2 AB = CG

AE = CG

2) √EAF = GCF ( alternate interior angles)

3). AF = FC. ( F is the mid point)

so by SAS congruence rule

∆ AEF congruent ∆ CGF

so EF=FG ........(1)

now in //gm EG =BC ( opposite sides of//gm are equal)

so, 1/2 EG = 1/2 BE

EF = 1/2 BE. #Ans