given that ba bisects ∠dbc, which statement must be true?\no m∠abd = m∠abc\no ab ≅ bc\no b is the mid…
given that ba bisects ∠dbc, which statement must be true?\no m∠abd = m∠abc\no ab ≅ bc\no b is the mid - point of dc.\no m∠dbc = 90°
Answer
Explanation:
Step1: Recall angle - bisector definition
An angle - bisector divides an angle into two equal angles. Since $\overrightarrow{BA}$ bisects $\angle DBC$, by the definition of an angle - bisector, $\angle ABD$ and $\angle ABC$ are the two angles formed by the bisector $\overrightarrow{BA}$ of $\angle DBC$. So, $m\angle ABD=m\angle ABC$.
Step2: Analyze other options
- For $\overline{AB}\cong\overline{BC}$, just because $\overrightarrow{BA}$ bisects $\angle DBC$ does not mean the sides are congruent. There is no information to suggest this.
- For $B$ being the mid - point of $\overline{DC}$, an angle - bisector of an angle at a vertex of a triangle does not necessarily bisect the opposite side.
- For $m\angle DBC = 90^{\circ}$, there is no information given to suggest that $\angle DBC$ is a right - angle.
Answer:
A. $m\angle ABD=m\angle ABC$