Question

State basic proportionality theorem. Use it to prove the following: If three parallel lines l, m, n are intersected by transversals q and s as shown in the adjoining figure, then $\frac{A B}{BC} = \frac{D E}{EF}$ .

Approach

Basic Proportionality Theorem: If a line is drawn parallel to one side of a triangle intersecting the other two sides, then it divides those sides in the same ratio. To prove $\frac{A B}{BC} = \frac{D E}{EF}$ : Consider the configuration with three parallel lines l, m, n cut by transversals q and s. Apply BPT to appropriate triangles formed, establishing the proportionality of segments.

Step-by-step working

1
State Basic Proportionality Theorem
1 mark
2
Identify triangles and parallel lines in the figure
1 mark
3
Apply BPT to show $\frac{A B}{BC} = \frac{D E}{EF}$
2 marks
4
Conclude the proof
1 mark

Concepts used

basic proportionality theoremparallel linestransversalsproportional segments

Approach

Step-by-step working

Concepts used

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