Question

Which of the following statements is true only if triangles EFI and GFH are similar?

Answer 1

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.

Answer 2

Answer:

B

Step-by-step explanation:

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