If triangle ABC sim triangle EDF and triangle | vedclass

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Question

(B) Given,$	riangle ABC \sim 	riangle EDF$.Therefore,the ratios of corresponding sides are equal:$\frac{AB}{ED} = \frac{BC}{DF} = \frac{AC}{EF}$.Fro

Vedclass · Accepted Answer

$BC \cdot DE = AB \cdot EF$

Vedclass · Answer

(B) Given,$	riangle ABC \sim 	riangle EDF$.Therefore,the ratios of corresponding sides are equal:$\frac{AB}{ED} = \frac{BC}{DF} = \frac{AC}{EF}$.From $\frac{AB}{ED} = \frac{BC}{DF}$,we get $AB \cdot DF = ED \cdot BC$,which is $BC \cdot DE = AB \cdot DF$. Thus,option $(d)$ is true.From $\frac{BC}{DF} = \frac{AC}{EF}$,we get $BC \cdot EF = AC \cdot DF$. This does not match any option directly,but let's check the others.From $\frac{AB}{ED} = \frac{AC}{EF}$,we get $AB \cdot EF = AC \cdot ED$,which is $AB \cdot EF = AC \cdot DE$. Thus,option $(a)$ is true.Comparing the given options with the derived ratios:Option $(a)$: $AB \cdot EF = AC \cdot DE$ (True)Option $(d)$: $BC \cdot DE = AB \cdot DF$ (True)Option $(b)$: $BC \cdot DE = AB \cdot EF$ (This is not derived from the similarity $	riangle ABC \sim 	riangle EDF$)Option $(c)$: $BC \cdot EF = AC \cdot FD$ (This is not derived from the similarity $	riangle ABC \sim 	riangle EDF$)Re-evaluating the question: The question asks which is $NOT$ true. Based on the similarity $	riangle ABC \sim 	riangle EDF$,the correct ratios are $\frac{AB}{ED} = \frac{BC}{DF} = \frac{AC}{EF}$.From this,$BC \cdot EF = AC \cdot DF$ is true. Option $(c)$ says $BC \cdot EF = AC \cdot FD$. Since $DF = FD$,option $(c)$ is also true.Therefore,option $(b)$ is the one that is not true.

If $\triangle ABC \sim \triangle EDF$ and $\triangle ABC$ is not similar to $\triangle DEF$,then which of the following is not true?

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