2026 · Basic · Set 3 · Part 1·Q33·5 marks
Triangles
Question
State and Prove "Basic Proportionality Theorem".
Approach
Statement: If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then it divides the two sides in the same ratio. Proof involves constructing perpendiculars and using area ratios to show .
Step-by-step working
- 1
Statement of Basic Proportionality Theorem
1 mark - 2
Draw triangle ABC with line DE parallel to BC
0.5 marks - 3
Construct perpendiculars from D and E to AB and AC respectively
1 mark - 4
Using area of triangles, show
2 marks - 5
Hence proved
0.5 marks
Concepts used
basic proportionality theoremthales theoremparallel linesproof
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