Question

in fig 2.21, A,B and C are points on OP,OQ and OR respectively such that AB // PQ and AC // PR show that BC//QR

Answer 1

Step-by-step explanation:

1. In ΔOQP

  AB ║ PQ , Then point A and B divide the line OP and OQ in same     ratio.

  So we can write in this way

  $\mathbf{\frac{OA}{OP}=\frac{OB}{OQ}}$             ...1)

2. In ΔOPR

  AC ║ PR , Then point A and C divide the line OP and OR in same     ratio.

  So we can write in this way

  $\mathbf{\frac{OA}{OP}=\frac{OC}{OR}}$             ...2)

3. We see that L.H.S is equal in equation 1) and equation 2). So R.H.S    

   should also be equal.

   $\mathbf{\frac{OB}{OQ}=\frac{OC}{OR}}$            ...3)

   Here $\mathbf{\frac{OB}{OQ}=\frac{OC}{OR}}$ in ΔOQR .Means BC║QR. This is it which we have to  

   prove.

 

Answer 2

Answer:

Step-by-step explanation:

1. In ΔOQP

  AB ║ PQ , Then point A and B divide the line OP and OQ in same     ratio.

  So we can write in this way

  \mathbf{\frac{OA}{OP}=\frac{OB}{OQ}}OPOA=OQOB             ...1)

2. In ΔOPR

  AC ║ PR , Then point A and C divide the line OP and OR in same     ratio.

  So we can write in this way

  \mathbf{\frac{OA}{OP}=\frac{OC}{OR}}OPOA=OROC             ...2)

3. We see that L.H.S is equal in equation 1) and equation 2). So R.H.S    

   should also be equal.

   \mathbf{\frac{OB}{OQ}=\frac{OC}{OR}}OQOB=OROC            ...3)

   Here \mathbf{\frac{OB}{OQ}=\frac{OC}{OR}}OQOB=OROC in ΔOQR .Means BC║QR. This is it which we have to  

   prove.