Question

given: m∠abc = m∠cbd prove: bc bisects ∠abd. justify each step in the flowchart proof. a: m∠abc = m∠cbd b: ∠abc ≅ ∠cbd c: bc bisects ∠abd a: given b: definition of congruent c: definition of congruent definition of bisect given reflexive property

Explanation:

Step1: Given information

We are given that $m\angle ABC = m\angle CBD$.

Step2: Use congruent - angle definition

If two angles have the same measure, by the definition of congruent angles, $\angle ABC\cong\angle CBD$.

Step3: Use angle - bisector definition

Since $\angle ABC$ and $\angle CBD$ are congruent and they share a common side $\overrightarrow{BC}$ and are adjacent, by the definition of an angle - bisector (a ray that divides an angle into two congruent adjacent angles), $\overrightarrow{BC}$ bisects $\angle ABD$.

Answer:

C: definition of bisect