Question

A and C divide the side PQ of angle PQR into three equal parts, AB||CDIIQR.
Prove that B and D also divide PR into three equal parts.​

Answer 1

Answer:

I think the information provided is not sufficient.

Answer 2

Answer:  

               Given: A and C divide the side PQ of ΔPQR into three parts.

∴AP = AC = CQ

And     AB║CD║QR             .........(i)

To Prove :         PB = BD = DR

Proof :        AB║CD║QR                  (Given)

In ΔPCD ,we have

                     AP = AC         (Given)

                      AB ║ CD        (Given)

Then,          PB = BD         ......(ii)

                                    (By Converse of mid point theorem)

Similarly,         AB║CD║QR

and                   AC = CQ

 ∴                     BD = DR     .......(iii)

                                                 (By equal intercept theorem)

From  equation (ii) and (iii)

                          PB = BD = DR                  ( Proved)