Question

In triangle PQR,if B and C are points on sides PR and QR respectively such that RB=10cm,PR=18cm RC=15cm and CQ=12cm then find whether BC is parallel to QR or not.

Answer 1

Solution:-
In Δ RPQ,
RP = 18 cm
RB = 10 cm
⇒ BP = RP - RB= 18 - 10 = 8 cm
Now, RC 15 cm
CQ = 12 cm
Now, RB/BP = 10/8 = 5/4
and RC/CQ = 15/12 = 5/4
⇒ RB/BP = RC/CQ
In triangle RPQ 
RB/BP = RC/CQ [Proved above]
Therefore, BC is parallel to PQ  [Converse of BPT]
Hence proved.

Answer 2

   There seems to be an error in the question...  We need to find whether BC is parallel to  PQ or not.

   If BC is parallel to PQ, that means that ΔPQR and ΔBCR are similar. Let us check that.

   We know  BR || PR,   CR || QR.  ∠R is common between the two.

   RQ = RC + CQ = 15 + 12 = 27 cm             PR = 18 cm
   BR = 10 cm             RC = 15 cm

So check the ratio of sides,
    BR/ PR = 10/18 = 5/9               CR/ QR = 15/27 = 5/9

  Since the ratio of corresponding sides is equal they are similar.  Hence, BC || PQ.