Answer:
Explanation:
To complete the proof that ∠EIF ≅ ∠GIH, we need to show that they are congruent or equal in measure. Here's a step-by-step explanation:
1. Given: ∠EIF and ∠GIH
2. We need to prove: ∠EIF ≅ ∠GIH
Proof:
Step 1: Draw a diagram of the given situation. This will help visualize the angles and their relationships.
Step 2: Identify any known angle relationships. Look for angles that are congruent, supplementary, or complementary. These relationships can help establish the congruence between ∠EIF and ∠GIH.
Step 3: Apply the angle congruence theorems. In this case, the Angle Bisector Theorem or Vertical Angles Theorem could be relevant. These theorems state that angles that share a common vertex and have equal measures are congruent.
Step 4: Determine if any angle bisectors or vertical angles are present in the given diagram. If there are, you can use them to prove the congruence of ∠EIF and ∠GIH.
Step 5: Apply the angle congruence theorem that is appropriate for the given situation. Use the known angle relationships and theorems to provide a clear and logical explanation for why ∠EIF and ∠GIH are congruent.
Step 6: Summarize the proof by stating that based on the identified angle relationships and theorems, ∠EIF and ∠GIH are congruent.
Please note that without the specific diagram and additional information about the angles and their relationships, it is not possible to provide a more specific proof. However, by following these steps and applying the relevant angle congruence theorems, you should be able to complete the proof successfully.