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

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

 

Answers (1)

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

Safeer PP

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