Question

I triangle abc ad is median ,o is any point on ad bo and co on producing meet ac and ab at e andf . Now ad is produced to x such that od=dx prove thatfe||bc

Answer 1

Proven that FE ║ BC

Given

To prove that FE ║ BC

From the figure :

Mid pont of BC and OX is "D".

AD, BO and CO intersects at "O".

It meets AC and AB at E and F respectively.

AD is extended to "X".

It forms a parallelogram OBXC.

In parallelogram OBXC,

                           BD = CD            OD = DX

                           BC and OX bisect each other.

Where,                BX ║ CO   and   CX ║ BO

                           BX ║ CF    and   CX ║ BE

                           BX ║ OF    and   CX ║OE

In ΔABX,   OF ║ BX

By using B.P.T ( Basic Proportionality Theorem ),

                         $\frac{AO}{AX}$  =  $\frac{AF}{AB}$    ------> ( 1 )  

In ΔACX,  OE ║ CX      

By using B.P.T,          

                          $\frac{AO}{AX}$  =  $\frac{AE}{AC}$    ------> ( 2 )

Compare the equation ( 1 ) and ( 2 ),

                         $\frac{AF}{AB}$  =  $\frac{AE}{AC}$

Therefore, applying converse of B.P.T, it has been proved that FE ║ BC.

To learn more...

1. brainly.in/question/7792235

2. brainly.in/question/4740950

Answer 2

OD=DX. BD=DC. bdco is a parallelogram. at triangle boc=are ab.c. bx parallel cf and bx parallel of. in triangle b. ao/x=af/ab. ab:ax=af:ab