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SashulF [63]
2 years ago
8

Which of the following is a true proportion of the figure based on the triangle proportionality theorem?

Mathematics
1 answer:
prisoha [69]2 years ago
6 0

Answer:

The correct option is A.

Step-by-step explanation:

When we have two congruent figures, the correspondent sides of the figures are related by the same constant C.

In the case of the image.

h is the left side of the smaller triangle.

h + j is the left side of the larger triangle.

Then we have the relation:

(h + j) = C*h

If we isolate C, we get:

C = (h + j)/h

We can also write this for the other side (the bottom one)

k*C = (k + i)

C = (k + i)/k

Then we have:

(h + j)/h = (k + i)/k

We can rewrite this as:

h/h + j/h = k/k + i/k

1 + j/h = 1 + i/k

We can subtract 1 in each side to get:

j/h = i/k

This is almost the same we can see in option A (its inversed)

If we apply the inverse to both sides, we get:

(j/h)^-1 = (i/k)^-1

h/j = k/i

Which is the same equation that we can see in option A.

Then the correct option is A.

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