Question

point b is the midpoint of ac. which statements about the figure must be true? (choose three correct answers.) db ≅ bc 2 m∠dbc = m∠abc bc = ½ ac ∠dbc is bisected by ray bd

Explanation:

Step1: Analyze the first option

Since there is no information given about the length of \(DB\) and \(BC\), we cannot say \(DB = BC\).

Step2: Analyze the second option

\(\angle ABC = 90^{\circ}\) (right - angle) and \(\angle DBC=90^{\circ}\), so \(m\angle DBC=m\angle ABC\).

Step3: Analyze the third option

Since \(B\) is the mid - point of \(AC\), by the definition of mid - point \(AB = BC\) and \(BC=\frac{1}{2}AC\).

Step4: Analyze the fourth option

\(\angle DBC\) is a single angle, not an angle that is bisected. There is no ray that splits \(\angle DBC\) into two equal parts.

Answer:

\(2m\angle DBC = m\angle ABC\), \(BC=\frac{1}{2}AC\)