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100 POINTS!!!! PLEASE HELP!! ITS DUE IN 1 HOUR!!!!!!!!!!!!!!

100 POINTS!!!! PLEASE HELP!! ITS DUE IN 1 HOUR!!!!!!!!!!!!!!-example-1

2 Answers

5 votes

Answer:


(4)/(3)

Explanation:

In similar triangles, corresponding angles are the same size. Therefore, if triangle ABC is similar to triangle DEF then:

  • ∠A ≅ ∠D
  • ∠B ≅ ∠E
  • ∠C ≅ ∠F

The standard convention is to label the sides of a triangle with lowercase letters that correspond to the vertices they are opposite to.

In similar triangles, corresponding sides are always in the same ratio. Therefore:

  • a : d = b : e = c : f

If similar triangles ABC and DEF have a scale ratio of 1/3, it means that each side of triangle ABC is 1/3 the length of the corresponding side in triangle DEF. Therefore, as side d is the corresponding side to side a:


\begin{aligned}\textsf{Length of $a$} &= \textsf{Scale ratio}* \textsf{Length of $d$} \\\\&=(1)/(3) * 4\\\\&=(4)/(3)\end{aligned}

So, the length of side d is 4/3 units.

User Guthrie
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8.4k points
5 votes
If the scale ratio of two similar triangles is 1/3, that means the corresponding sides of the two triangles are in the same ratio.

If side 'd' of triangle DEF has a length of 4, and the scale ratio of the two triangles is 1/3, then the length of the corresponding side 'a' of triangle ABC can be found as follows:

a/d = 1/3

a = (1/3)d

a = (1/3)4

a = 4/3

Therefore, the length of side 'a' is 4/3.
User Xtrinch
by
7.6k points

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