Question

State and prove Basic Proportionality Theorem.

Approach

State and prove Basic Proportionality Theorem: If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio. Full marks for correct statement (1 mark), correct given/to prove/construction/figure (2 marks), and rigorous proof (2 marks).

Step-by-step working

1
Statement: If DE is parallel to BC in triangle ABC, then $\frac{A D}{D B} = \frac{A E}{EC}$
1 mark
2
Given, To Prove, Construction, and Figure
2 marks
3
Proof using area ratios and parallel line properties
2 marks

Concepts used

trianglesbasic proportionality theoremthales theoremprovemedianssimilar triangles

Approach

Step-by-step working

Concepts used

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