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  • If the areas of two similar triangles are equal, prove that they are congruent.

Q4   If the areas of two similar triangles are equal, prove that they are congruent.

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best_answer

Let \triangle ABC\, \sim \, \triangle DEF, therefore,

ar(\triangle ABC\,) = \,ar( \triangle DEF)                (Given )

\frac{ar(\triangle ABC)}{ar(\triangle DEF)}=\frac{AB^2}{DE^2}=\frac{BC^2}{EF^2}=\frac{AC^2}{DF^2}................................1

\therefore \frac{ar(\triangle ABC)}{ar(\triangle DEF)}=1

\Rightarrow \frac{AB^2}{DE^2}=\frac{BC^2}{EF^2}=\frac{AC^2}{DF^2}=1

AB=DE

BC=EF

AC=DF

\triangle ABC\, \cong \, \triangle DEF                    (SSS )

 

 

 

 

 

Posted by

seema garhwal

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