Answer:The question is asking you to prove that ∠EFGI is congruent to ∠FGHI. Here’s how you can do it:
Given: This is the information that the problem provides you with. In this case, it’s the diagram of the parallelogram with the marked angles.
∠EG ≅ ∠FG: This is given in the problem.
∠EGI ≅ ∠FGH: This is also given in the problem.
Alternate Interior Angles are congruent: This is a theorem in geometry that states if two parallel lines are cut by a transversal, then the alternate interior angles are congruent. In this case, since EFGI and FGHI are parallelograms, ∠EGI and ∠FGH are alternate interior angles, so they are congruent.
∠EFGI ≅ ∠FGHI: This is what you’re trying to prove. Since ∠EG ≅ ∠FG (from step 2) and ∠EGI ≅ ∠FGH (from step 3), you can say that ∠EFGI ≅ ∠FGHI because corresponding parts of congruent triangles are congruent (CPCTC).