Question

prove that the ratio of the perimeters of two similar triangles is the same as the ratio of their corresponding sides with a suitable diagram.

Answer 1

Answer:

Step-by-step explanation:

Answer 2

The proving of the given scenario is described below.

Step-by-step explanation:

In ΔABC and ΔXYZ,

If ABC $\sim$ XYZ

When the corresponding sides of a triangle are similar, then

⇒  $\frac{AB}{XY} =\frac{BC}{YZ} =\frac{AC}{XZ} =K$

from the above equation, we get

⇒  $AB=K\times XY$...(equation 1)

⇒  $BC=K\times YZ$...(equation 2)

⇒  $AC=K\times XZ$...(equation 3)

On adding the equation 1, equation 2, equation 3, we get

⇒  $AB+BC+AC=K(XY+YZ+XZ)$

⇒  $\frac{AB+BC+AC}{XY+YZ+XZ}=K$

⇒  $\frac{Perimeter \ of \ \Delta ABC}{Perimeter \ of \ \Delta XYZ}$

⇒  $\frac{AB}{XY} =\frac{BC}{YZ} =\frac{AC}{XZ}$

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