Question 107
The following figure shows a triangle $A B C$, two squares $A B D E$ and $A C F G$, both constructed on the sides of triangle $A B C$, and another triangle $A E G$.
We say that triangles $A B C$ and $A E G$, positioned in this way relative to two squares, are sibling triangles.
a. Verify that $\angle B A C+\angle G A E=180^\circ$.
b. After verifying the previous item, we can rotate triangle $A E G$ by $90^\circ$ counterclockwise about $A$ to reach the position $B A G'$. It is worth noting that $B A=A E$, since they are sides of the square $A B D E$. From this, prove that the sibling triangles $A B C$ and $A E G$ have the same area.
We say that triangles $A B C$ and $A E G$, positioned in this way relative to two squares, are sibling triangles.
a. Verify that $\angle B A C+\angle G A E=180^\circ$.
b. After verifying the previous item, we can rotate triangle $A E G$ by $90^\circ$ counterclockwise about $A$ to reach the position $B A G'$. It is worth noting that $B A=A E$, since they are sides of the square $A B D E$. From this, prove that the sibling triangles $A B C$ and $A E G$ have the same area.