Question

The perimeters of similar triangles are in the same ratio as the corresponding sides

Answer 1

Answer:

Always

Step-by-step explanation:

Suppose you have triangle ABC with side lengths a, b, c. Suppose that is similar to triangle DEF with side lengths d, e, f.

Now, let k be the ratio of corresponding sides ...

  k = d/a

Because the same factor applies to all sides, we also have ...

  k = e/b = f/c

That is, if we multiply by the denominators of each of these fractions, we get ...

• d = a·k
• e =b·k
• f = c·k

The perimeter of ΔABC is ...

   perimeter(ABC) = a + b + c

The perimeter of ΔDEF is ...

  perimeter(DEF) = d + e + f = a·k + b·k + c·k

  perimeter(DEF) = k(a + b + c) = k·perimeter(ABC)

  k = perimeter(DEF)/perimeter(ABC)

That is, the perimeters are in the same ratio as corresponding sides.