Question

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

Line segments EG and HI intersect at point F, forming triangles EFI and HFG. Line a intersects with both triangles at point F.

two segment FI equals three segment FH
segment FH over segment FI equals segment HG over segment IE
Points E, F, and G are collinear
∠F ≅ ∠F

Answer 1

For triangles EFI and GFH to be similar, the statement 'segment FH over segment FI equals segment HG over segment IE' must be true.

Step-by-step explanation:

In order for triangles EFI and GFH to be similar, the following statement must be true: segment FH over segment FI equals segment HG over segment IE.

This can be illustrated as:

FI = x (let's say)

FH = 2x (since two segment FI equals three segment FH)

HG = 2 (let's say)

IE = 1 (since points E, F, and G are collinear, IE can be represented as 1)

So, segment FH over segment FI (2x/x) equals segment HG over segment IE (2/1), which fulfills the condition for similarity between triangles EFI and GFH.