Questions: If BC bisects the angle ACD, then B is the midpoint of AD. A. True B. False

Solution Steps

The problem states that line segment \( \overline{BC} \) bisects the angle \( \angle ACD \). We need to determine if this implies that point \( B \) is the midpoint of line segment \( \overline{AD} \).

An angle bisector divides an angle into two equal parts. In this case, \( \overline{BC} \) divides \( \angle ACD \) into two equal angles, \( \angle ACB \) and \( \angle BCD \).

The fact that \( \overline{BC} \) bisects \( \angle ACD \) does not provide any information about the lengths of \( \overline{AD} \) or the position of point \( B \) on \( \overline{AD} \). Therefore, we cannot conclude that \( B \) is the midpoint of \( \overline{AD} \) based solely on the angle bisector.

Final Answer