Question

Which of the following sets of data make FG parallel AB=14, AF=6, AC=7, AG=3

b) AB=12, FB=3, AC=8, AG=6

c) AB=10, AF=5, AC=20, AG=4

d) AF=6, FB=5, AG=9, GC=8

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Answer 1

$\underline{\pink{Converse \:of \: Basic \: Proportionality \: Theorem :}}$

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

$a) Here ,In \: \triangle ABC ,$

$AB = 14, AF = 6 ,AC = 7 AG = 3$

$i) \frac{AB}{AF} = \frac{14}{6} = \frac{7}{3}$

$ii) \frac{AC}{AG} = \frac{7}{3}$

$\frac{AB}{AF} = \frac{AC}{AG}$

$\therefore \green { FG /parallel BC }$

$b) Here ,In \: \triangle ABC ,$

$AB=12, FB=3, AC=8, AG=6$

$GC = AC - AG$

$= 8 - 6 = 2$

$i) \frac{AB}{FB} = \frac{12}{3} = 4$

$ii) \frac{AC}{GC} =\frac{ \frac{8}{2} = 4$

$\frac{AB}{FB} = \frac{AC}{GC}$

$\therefore \green { FG /parallel BC }$

$c) Here ,In \: \triangle ABC ,$

$AB=10, AF=5, AC=20, AG=4$

$i) \frac{AB}{AF} = \frac{10}{5} = 2$

$ii) \frac{AC}{AG} = \frac{20}{4} = 5$

$\frac{AB}{AF} \neq \frac{AC}{AG}$

$\therefore \red { FG \:not \: parallel \:to \:BC }$

$d) Here ,In \: \triangle ABC ,$

$AF=6, FB=5, AG=9, GC=8$

$i) \frac{AF}{FB} = \frac{6}{5}$

$ii) \frac{AG}{GC} = \frac{9}{8}$

$\frac{AF}{FB} \neq \frac{AG}{GC}$

$\therefore \red { FG \:not \: parallel \:to \:BC }$

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