Question

Which of the following statements are enough to prove that 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.

A. segment FI = segment FH
B. segment EI over segment FI = segment GH over segment FH
C. ∠E ≅ ∠G
D. Segments EG and IH intersect at point F

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

Since the image tells us that <F is congruent to <F in both triangles, an additional statement that would be enough to prove that$\triangle EFI and \triangle GFH$ are similar by the AA Similarity Postulate is: C. $\mathbf{\angle E \cong \angle G}$

Recall:

Vertical angles have equal angle measure.

If we know that two angles in one triangle are congruent to two angles in another triangle, we can prove that the two triangles are similar by the Angle-Angle (AA) Similarity Postulate.

From the image given, we know that:

<F in $\triangle EFI$ is congruent to <F in $\triangle GFH$ because they are both vertically opposite to each other.

Therefore if we know that $\angle E \cong \angle G$, we can now prove that $\triangle EFI and \triangle GFH$ are similar because they have two corresponding angles that are congruent .

Therefore, since the image tells us that <F is congruent to <F in both triangles, an additional statement that would be enough to prove that$\triangle EFI and \triangle GFH$ are similar by the AA Similarity Postulate is: C. $\mathbf{\angle E \cong \angle G}$

Learn more here:

https://brainly.com/question/2269451