Question

State the converse of basic proportionality theorem.

Also find $\frac{BF}{FC}$ in the following figure, given that $A B ∥ D C ∥ EF$ and $\frac{A E}{E D} = \frac{2}{3}$ . Also, find the length of EF if $A B = 10$ cm and $D C = 15$ cm.

Approach

Converse: If a line divides two sides of a triangle proportionally, it's parallel to the third side. Using intercept theorem: $\frac{BF}{FC} = \frac{A E}{E D} = \frac{2}{3}$ . For EF: by proportionality, $EF = 12$ cm.

Step-by-step working

1
State converse theorem
1 mark
2
$\frac{BF}{FC} = \frac{2}{3}$
2 marks
3
Calculate EF = 12 cm
2 marks

Concepts used

basic proportionality theoremparallel linessimilar triangles

Approach

Step-by-step working

Concepts used

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