Question

given: ( mangle abc = mangle cbd ) prove: ( overrightarrow{bc} ) bisects ( angle abd ). justify each step in the flowchart proof. a: b: c:

Explanation:

• For step A: The given information is \( m\angle ABC = m\angle CBD \), so the justification is "Given".
• For step B: If the measures of two angles are equal, then the angles are congruent. This is the definition of congruent angles (angles with equal measure are congruent), so the justification is "Definition of Congruent Angles (If \( m\angle 1 = m\angle 2 \), then \( \angle 1\cong\angle 2 \))".
• For step C: A ray bisects an angle if it divides the angle into two congruent angles. Since \( \angle ABC\cong\angle CBD \), \( \overrightarrow{BC} \) divides \( \angle ABD \) into two congruent angles, so the justification is "Definition of Angle Bisector (A ray bisects an angle if it divides the angle into two congruent angles)".

Answer:

• A: Given
• B: Definition of Congruent Angles (If \( m\angle 1 = m\angle 2 \), then \( \angle 1\cong\angle 2 \))
• C: Definition of Angle Bisector (A ray bisects an angle if it divides the angle into two congruent angles)