To prove angle GEA is congruent to angle AIG, we can use the SAS Postulate since EG is congruent to IA and angle EGA is congruent to angle IAG. Additionally, ASA Congruence Theorem confirms the triangles EGA and IAG are congruent, making all corresponding angles congruent, including angle GEA and angle AIG.
To prove that angle GEA is congruent to angle AIG, we must first understand that congruent triangles have congruent corresponding angles.
In the problem, it is given that EG is congruent to IA, and angle EGA is congruent to angle IAG.
These congruences provide information about two sides and the included angle of the potential triangles, suggesting they could be congruent by the SAS Postulate (Side-Angle-Side).
Here is a step-by-step explanation to fill in the stated proof lines:
EG is congruent to IA (given).
Angle EGA is congruent to angle IAG (given).
Angle GEA is congruent to angle AIG (by ASA Congruence Theorem, as the two angles and the included side between them are congruent).
Therefore, by the ASA Congruence Theorem (which states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent), triangles EGA and IAG are congruent.
Hence, all corresponding angles of the triangles are congruent, which includes angle GEA being congruent to angle AIG.