Prove that the ratio of the perimeters of two similar triangles is same as the ratio of their corresponding sides

Asked by Pratima | 25th Sep, 2015, 11:57: AM

Expert Answer:

 
 
 
begin mathsize 14px style Let space the space two space similar space triangles space be space increment ABC space and space increment PQR When space the space triangles space are space similar comma 1. space The space corresponding space angles space are space equal 2. space Their space corresponding space sides space are space proportional. Hence comma space in space increment ABC space and space increment PQR. AB over PQ equals BC over QR equals AC over PR space space space  The space perimetr space of space increment ABC space equals AB space plus BC plus AC space space space... left parenthesis 2 right parenthesis The space perimetr space of space increment PQR space equals PQ plus QR plus PR space space... left parenthesis 3 right parenthesis  because AB over PQ equals BC over QR equals AC over PR equals space fraction numerator AB plus BC plus AC over denominator PQ plus QR plus PR end fraction space space space left parenthesis Property space of space ratio space and space proportion right parenthesis space therefore AB over PQ equals BC over QR equals AC over PR equals space fraction numerator AB plus BC plus AC over denominator PQ plus QR plus PR end fraction equals fraction numerator space Perimetr space of space increment ABC over denominator Perimetr space of space increment PQR end fraction space space space space... left parenthesis 2 right parenthesis space and space... left parenthesis 3 right parenthesis end style

Answered by Priti Shah | 25th Sep, 2015, 12:52: PM

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