(Solved): 3) Study the proof that shows why the construction to bisect an angle works (Section 4.3, Example 3 ...

3) Study the proof that shows why the construction to bisect an angle works (Section 4.3, Example 3.6, pg 93) Given: \( B R=B S \) since we drew a circle, center \( \theta \) (anyradius) \( R X=5 X \leftarrow \begin{array}{l}\text { since we drew } \\ \text { circles, centers } R\end{array} \) Prove: \( a=b \) (same radius) (which shows \( \overrightarrow{B X} \) bisects \( \angle A B C \) ) DO THE PROOF \( (a) \) Given: \( A B=B C \) \( B D=B E \) Prove: \( A D=E C \) (b) Given: \( A C=B D \) Prove: \( \angle D B C=\angle A C B \) and \( A B=D C \)