Exercise 49 Page 558

Practice makes perfect

a Let's start with evaluating the ratio of the corresponding sides of these similar triangles.

a/3a=b/3b=c/3c=1/3 Now, we will evaluate the ratio of perimeters of △ FGH and △ XYZ.

a+b+c/3a+3b+3c

FactorOut

Factor out 3

a+b+c/3(a+b+c)

ReduceFrac

a/b=.a /(a+b+c)./.b /(a+b+c).

1/3

As we can see, the perimeters of these triangles have the same ratio, 13, as the corresponding sides.

b Let's now check what is the ratio of the corresponding sides if we add 6 to the lengths of each side.

a+ 6/3a+ 6=b+ 6/3b+ 6=c+ 6/3c+ 6 Now, we will evaluate the ratio of perimeters of △ FGH and △ XYZ.

(a+ 6)+(b+ 6)+(c+ 6)/(3a+ 6)+(3b+ 6)+(3c+ 6)

AddTerms

Add terms

a+b+c+18/3a+3b+3c+18

As we can see, the perimeters of these triangles do not have the same ratio as the corresponding sides. Therefore, the new triangles are not similar.

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Exercises p.554-559

Exercise 49 Page 558

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