In Delta ABC and Delta DEF,frac{AB}{DF} = fra | vedclass

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(C) Given that in $\Delta ABC$ and $\Delta DEF$,we have $\frac{AB}{DF} = \frac{BC}{EF}$ and $\angle B = \angle F$.According to the $SAS$ (Side-Angle-S

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$SAS$

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(C) Given that in $\Delta ABC$ and $\Delta DEF$,we have $\frac{AB}{DF} = \frac{BC}{EF}$ and $\angle B = \angle F$.According to the $SAS$ (Side-Angle-Side) similarity criterion,if one angle of a triangle is equal to one angle of another triangle and the sides including these angles are proportional,then the two triangles are similar.Here,the sides $AB$ and $BC$ include $\angle B$,and the sides $DF$ and $EF$ include $\angle F$.Since the ratios of the sides are equal and the included angles are congruent,the correspondence $ABC \leftrightarrow DFE$ is a similarity by the $SAS$ condition.

In $\Delta ABC$ and $\Delta DEF$,$\frac{AB}{DF} = \frac{BC}{EF}$ and $\angle B \cong \angle F$. Then,by $\ldots \ldots \ldots$ condition,the correspondence $ABC \leftrightarrow DFE$ is a similarity.

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