Let $P$ and $Q$ denote planes in 3 dimensional Euclidean space whose intersection is a line $L$. Let $A, A', B, B'$ be points on $L$ such that $A\neq B$ and $A'\neq B'$. Let $C$ be a point on $P$ that is not on $L$, and let $D$ be a point on $Q$ that is not on $L$. Define $C'$ to be the unique point on $P$ on the same side of $L$ as $C$, such that $\angle B'A'C'$ is congruent to $\angle BAC$, and define $D'$ to be the unique point on $Q$ on the same side of $L$ as $D$ such that $\angle B'A'D'$ is congruent to $\angle BAD$. Are the angles $\angle CAD$ and $\angle C'A'D'$ congruent? If so, how can it be proved?
