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

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

 

 

Answers (1)

Let \: \: \Delta ABC \sim \Delta PQR\\\\\therefore \frac{Ar\: \: (\Delta ABC )}{Ar \: \: (\Delta ABC )} = \frac{AB^2}{PQ^2}= \frac{BC^2}{QR^2} = \frac{AC^2}{PR^2}

Given that ar\: \Delta ABC =ar\: \Delta PQR

so, 

1 = \frac{AB^2}{PQ^2}= \frac{BC^2}{QR^2} = \frac{AC^2}{PR^2}\\\\ AB = PQ , BC = QR , AC = PR

Hence corresponding sides are equal 

therefore \Delta ABC \cong \sim \Delta PQR

Hence proved 

Posted by

Safeer PP

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