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Which of the following statements is true only if triangles EFI and GFH are similar?
A two segment FI equals three segment FH
B segment FH over segment FI equals segment HG over segment IE
C Points E, F, and G are collinear
D ∠F ≅ ∠G

Which of the following statements is true only if triangles EFI and GFH are similar A two segment FI equals three segment FH B segment FH over segment FI equals class=

Respuesta :

Answer: Choice B

FH/FI = HG/IE

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Explanation:

We're told that triangles EFI and GFH are similar. The order of the lettering is important because it tells us how the angles pair up.

  • E and G pair up because they are the first letters of EFI and GFH
  • F and F pair up as they are the second letters
  • I and H pair up because they are the third letters

This means

  • E = G
  • F = F
  • I = H

Furthermore, it means

  • EF corresponds to FG
  • FI corresponds to FH
  • IE corresponds to GH

Focus on the last two items of the list above. We can then form the proportion

FI/FH = IE/GH

which is the same as

FH/FI = GH/IE

when we apply the reciprocal to both sides. Since HG is the same as GH, we can then say

FH/FI = HG/IE

So basically the corresponding sides create equal ratios to form this proportion. There are many other proportions that can be formed.

akposevictor

The statement that would be true if triangle EFI and triangle GFH are similar triangles is: [tex]\mathbf{ \frac{FH}{FI} = \frac{HG}{IE} }[/tex]

Recall:

Similar triangles will always have the same shape but different sizes.

The corresponding side lengths of two triangles that are similar are always proportional.

All three angles in one triangle are all congruent to all three corresponding angles in the other triangle it is similar to.

  • Thus:

If triangle EFI and triangle GFH are similar, therefore:

<E ≅ <G; <F ≅ <F; <I ≅ <H

  • Also:

[tex]\frac{GF}{EF} = \frac{HG}{IE} = \frac{FH}{FI}[/tex]

Therefore, the statement that would be true if triangle EFI and triangle GFH are similar triangles is: [tex]\mathbf{ \frac{FH}{FI} = \frac{HG}{IE} }[/tex]

Learn more here:

https://brainly.com/question/11780810

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