Question 102
Consider a triangle $ABC$ and squares $ABDE$ and $ACFG$ constructed externally on its sides. The segments $BG$ and $EC$ intersect at $P$.
a) Prove that triangles $BAG$ and $EAC$ are congruent.
b) Since these two triangles are congruent and have the point $A$ in common, we can rotate one of them about the point $A$ to obtain the other. Determine the angle of rotation and compute the angle $\angle BPC$.
a) Prove that triangles $BAG$ and $EAC$ are congruent.
b) Since these two triangles are congruent and have the point $A$ in common, we can rotate one of them about the point $A$ to obtain the other. Determine the angle of rotation and compute the angle $\angle BPC$.