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  • Two sides and the perimeter of one triangle are respectively three times the corresponding sides and the perimeter of the other triangle. Are the two triangles similar? Why?

Two sides and the perimeter of one triangle are respectively three times the corresponding sides and the perimeter of the other triangle. Are the two triangles similar? Why?

Answers (1)

Answer: True

According to the question,

AB = 3PQ \; \; \; \; \; \; ...(1)

AC = 3PR \; \; \; \; \;...(2)

also, the perimeter of \DeltaABC is three times the perimeter of \DeltaPQR

AB + BC + CA = 3(PQ + QR + RP)

AB + BC + CA = 3PQ + 3QR + 3RP

3PQ + BC + 3PR = 3PQ + 3QR + 3PR                   (using eq. (1) and (2))   

BC=3QR\; \; \; \; \; \; .....(3)

from equations (1), (2), and (3) we conclude that the sides of both triangles are in the same ratio.

As we know if the corresponding sides of two triangles are in the same ratio, then the triangles are similar by the SSS similarity criterion

Hence, the given statement is true.

Posted by

infoexpert23

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