Question

state and prove midpoint theorem ​

Answer 1

construction draw a parallel line CG of EB extend the line EF.

proof In AEF and CFF

angle1=angle2

AF=FC

angle3=angle4(vertically opposite angle)

aedis congruent to CGF (ASA)

EF=FG(by CPCT)

EA=CG(byCPCT)

BE=CG(parallel)

Therefore BCGE is a parallelogram

BC=EF

BCparallel EG

we know that EG=EF+FG

so we can say that it is 2EF

BC=2EF

1/2BC=EF

hence proved