Question

given ( mangle abc = mangle cbd ) prove ( overrightarrow{bc} ) bisects ( angle abd ) justify each step in the flowchart proof a ( mangle abc = mangle cbd ) b ( angle abccongangle cbd ) c ( overrightarrow{bc} ) bisects ( angle abd ) a b c definition of congruent definition of bisect given reflexive property

Explanation:

Step1: Identify the first step

The first step \(m\angle ABC = m\angle CBD\) is given in the problem statement, so A is "given".

Step2: Identify the second step

When two angles have equal measures (\(m\angle ABC = m\angle CBD\)), by the definition of congruent angles (angles are congruent if and only if their measures are equal), \(\angle ABC\cong\angle CBD\). So B is "definition of congruent".

Step3: Identify the third step

By the definition of an angle - bisector (a ray that divides an angle into two congruent adjacent angles). Since \(\angle ABC\cong\angle CBD\) and they are adjacent angles with common side \(\overrightarrow{BC}\) and common vertex \(B\), \(\overrightarrow{BC}\) bisects \(\angle ABD\). So C is "definition of bisect".

Answer:

A: given; B: definition of congruent; C: definition of bisect