If $\Delta ABC \sim \Delta EDF$ and $\Delta ABC$ is not similar to $\Delta DEF$, then which of the following is NOT true?
(a) $BC \cdot EF = AC \cdot FD$
(b) $AB \cdot EF = AC \cdot DE$
(c) $BC \cdot DE = AB \cdot EF$
(d) $BC \cdot DE = AB \cdot FD$
Step-by-Step Solution
Key Concept: From $\Delta ABC \sim \Delta EDF$, ratio of corresponding sides is $\dfrac{AB}{ED} = \dfrac{BC}{DF} = \dfrac{AC}{EF}$.
From $\dfrac{AB}{ED} = \dfrac{BC}{DF} = \dfrac{AC}{EF}$: cross-multiplying gives $AB \cdot DF = BC \cdot ED$, $AB \cdot EF = AC \cdot ED$, $BC \cdot EF = AC \cdot DF$ is NOT true. [0.5 Mark]
Hence $BC \cdot EF = AC \cdot FD$ is not true. [0.5 Mark]
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🎯 Official CBSE Marking Scheme:
Setting up similarity ratios: 0.5 Mark
Identifying false statement: 0.5 Mark
Correct Answer: $BC \cdot EF = AC \cdot FD$