Question

Which of the following statements are enough to prove that triangles EFI and GFH are similar?

Answer 1

To Prove: ΔEFI ~ Δ GFH

Proof:

When two triangles are similar, their corresponding sides are Proportional and their corresponding interior angles are equal.

Two Triangles can be proven similar by following Similarity Criterion.

1. AA

2.SSS

3.SAS

→∠EFI=∠GFH-------[Vertically Opposite angles]

The Other statement which is needed to prove that triangles EFI and GFH are similar is

 Option C:→  ∠E ≅ ∠G

So, Two triangles ΔEFI and Δ GFH are Similar by Angle-Angle(AA) Criterion.

Answer 2

Answer:

C. ∠E ≅ ∠G

Step-by-step explanation:

When we have to demonstrate a similarity between triangles, we don't use congruence postulates, because similarity is different that congruence. When we talk about similarity, we are using proportions. So, two similar triangles are proportional, not equal, this means that sides are not equal, only proportional, but angles between triangle are equal.

So, in this case, option C offers enough to prove a similarity. They are equal because they are alternate interior angles. Also, the common vertex F make angles EFI and GFH equal too, because those are opposite angles. At last, angle H and angle I are also equal, because if two angles are equal, the third also it is.

Therefore, as you can see, option C gives a window to a demonstration. So, based on this reasoning, we can say that both triangles are similar by Angle-Angle postulate.