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

__ Options__:

- 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 ≅ ∠G

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

__ Options__:

- 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 ≅ ∠G

+1 vote

Best answer

If triangles EFI and GFH are similar then, the statement

is correct.

__ Solution__:

The triangles EFI and GFH are similar. So, their corresponding angles are congruent and the corresponding sides are in proportion.

So,

EF corresponds to GF

FI corresponds to FH

IE corresponds to HG

Using properties of similarity of triangle, we can say;

FI/FH = IE/HG

which is the same as

FH/FI = HG/IE

Basically, the corresponding sides create equal ratios to form this proportion.

So,

Hence, proved.