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Similar Triangles: Converse of Proportionality Theorem
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Similar Triangles: Converse of Proportionality Theorem
You know that the converse of the basic proportionality theorem is true.
Example: For fig.1, state if PQ EF.
Solution: DP/DE = 3.9/3 = 13/10 and
DQ/QF = 3.6/2.4 = 3/2

As DP/DE DQ/QF
therefore, PQ is not parallel to EF.


Example: In fig.2, EF || AB || DC.
Prove that
AE/ED = BF/FC
Solution: From ADC, we have
EP DC (EF DC given)
Therefore, AE/ED = AP/PC (1)
Also, from CAB, we have
FP BA (EF AB given)
Therefore, BF/FC = AP/PC
Therefore, from (1) and (2),
AE/ED = BF/FC
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