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Provide the missing betweenness arguments to complete Euclid's proof of ( 1.7 ) in the case he considers. Namely, assuming that the ray $\overrightarrow{A D}$ ...

Question

Provide the missing betweenness arguments to complete Euclid's proof of ( 1.7 ) in the case he considers. Namely, assuming that the ray $\overrightarrow{A D}$ is in the interior of the angle $\angle C A B,$ and assuming that $D$ is outside the triangle $A B C,$ prove that $\overrightarrow{C B}$ is in the interior of the angle $\angle A C D$ and $\overrightarrow{D A}$ is in the interior of the angle $\angle C D B$ (FIGURE CAN'T COPY)

Provide the missing betweenness arguments to complete Euclid's proof of ( 1.7 ) in the case he considers. Namely, assuming that the ray $\overrightarrow{A D}$ is in the interior of the angle $\angle C A B,$ and assuming that $D$ is outside the triangle $A B C,$ prove that $\overrightarrow{C B}$ is in the interior of the angle $\angle A C D$ and $\overrightarrow{D A}$ is in the interior of the angle $\angle C D B$ (FIGURE CAN'T COPY)



Answers

Copy everything shown and complete the proof of Theorem 2-7 for the case where two angles are supplements of the same angle.
Given: $\angle 1$ and $\angle 5$ are supplementary;
$\angle 3$ and $\angle 5$ are supplementary.
Prove: $\angle 1 \cong \angle 3$


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