Similar Triangles: Converse of Proportionality Theorem

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 andDQ/QF = 3.6/2.4 = 3/2As 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 haveEP DC (EF DC given)Therefore, AE/ED = AP/PC (1) Also, from CAB, we have FP BA (EF AB given) Therefore, BF/FC = AP/PCTherefore, from (1) and (2), AE/ED = BF/FC
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