Question

Which of the following sets of data make FG || BC?

(i) AB = 14, AF = 6, AC = 7, AG = 3.

(ii) AB = 12, FB = 3, AC = 8, AG = 6.

(iii) AF = 6, FB = 5, AG = 9, GC = 8.

Answer 1

The given figure is:

(i) AB = 14, AF = 6, AC = 7 and AG = 3

Here, and.

Thus, by the corollary of Basic Proportionality Theorem, we have FG || BC.

(ii) AB = 12, FB = 3, AC = 8 and AG = 6

Now, AF = AB –FB = 12 –3 = 9

Here, and.

Thus, by the corollary of Basic Proportionality Theorem, we have FG || BC.

(iii) AF = 6, FB = 5, AC = 9 and GC = 8

Now, AB = AF + FB = 6 + 5 = 11 and AC = AG + GC = 9 + 8 = 17

Here, and.

Hence, from (i) and (ii), FG || BC