Prove that the ratio of the perimeter of 2 similar triangle is equal to the ratio of their corresponding sides.
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WE KNOW THAT IF TWO TRIANGLES ARE SIMILAR THEN THE RATIO OF THEIR CORRESPONDING SIDES ARE EQUAL.
HENCE IF TRIANGLE ABC IS SIMILAR TO PQR WE HAVE
AB/PQ=BC/QR=AC/PR
NOW USING A PROPERTY OF RATIOS
AB/PQ=BC/QR=AC/PR=AB+BC+CA/PQ+QR+PR
HENCE THE RATIO OF PERIMETER OF TWO SIMILAR PERIMETERS IS EQUAL TO THE RATIO OF CORRESPONDING TWO SIDES
HENCE IF TRIANGLE ABC IS SIMILAR TO PQR WE HAVE
AB/PQ=BC/QR=AC/PR
NOW USING A PROPERTY OF RATIOS
AB/PQ=BC/QR=AC/PR=AB+BC+CA/PQ+QR+PR
HENCE THE RATIO OF PERIMETER OF TWO SIMILAR PERIMETERS IS EQUAL TO THE RATIO OF CORRESPONDING TWO SIDES
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