Question

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

Explanation:

• A: The statement \(m\angle ABC = m\angle CBD\) is provided at the start of the problem, so it is "given".
• B: By the definition of congruent angles (if two angles have the same measure, they are congruent), since \(m\angle ABC = m\angle CBD\), we can say \(\angle ABC\cong\angle CBD\).
• C: By the definition of a bisector (a ray that divides an angle into two congruent adjacent angles), since \(\angle ABC\cong\angle CBD\), \(\overrightarrow{BC}\) bisects \(\angle ABD\).

Answer:

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