# In Fig. 6.21, A, B and C are points on OP, OQ, and OR respectively such that AB || PQ and AC || PR. Show that BC || QR

**Solution:**

As we know If a line divides any two sides of a triangle in the same ratio, then the line is parallel to the third side.

In ΔOPQ

AB || PQ (given)

OA/AP = OB/BQ.........(i) [∵ Thales Theorem(BPT)]

In ΔOPR

AC || PQ(given)

OA/AP = OC/CR............. (ii) [∵ Thales Theorem(BPT)]

From (i) & (ii)

OA/AP = OB/BQ = OC/CR

OB/BQ = OC/CR

Now, In ΔOQR

OB/BQ = OC/CR

BC || QR [∵ Converse of BPT]

**Video Solution:**

## In Fig. 6.21, A, B and C are points on OP, OQ, and OR respectively such that AB || PQ and AC || PR. Show that BC || QR

### Class 10 Maths NCERT Solutions - Chapter 6 Exercise 6.2 Question 6:

In Fig. 6.21, A, B and C are points on OP, OQ, and OR respectively such that AB || PQ and AC || PR. Show that BC || QR

Hence it is proved BC || QR if A, B and C are points on OP, OQ, and OR respectively such that AB || PQ and AC || PR