Question

1. if de is the perpendicular bisector of ac, which of the following statements is not true? ∠abd≅∠cbd ad≅cd bd≅be ab≅bc

Explanation:

Step1: Recall the properties of perpendicular bisector

A perpendicular bisector of a segment divides the segment into two equal parts. So, if \(DE\) is the perpendicular bisector of \(AC\), then \(AB = BC\) (by the definition of bisector). Also, by the SSS (Side - Side - Side) congruence criterion, \(\triangle ABD\cong\triangle CBD\) (since \(AB = BC\), \(BD=BD\) (common side), and \(AD = CD\) (any point on the perpendicular bisector of a segment is equidistant from the endpoints of the segment)). So, \(\angle ABD\cong\angle CBD\) and \(\overline{AD}\cong\overline{CD}\), \(\overline{AB}\cong\overline{BC}\)

Step2: Analyze \(\overline{BD}\cong\overline{BE}\)

There is no information given in the problem (such as \(DE\) being a bisector of \(BD\) or any congruent triangles involving \(BD\) and \(BE\)) to suggest that \(BD = BE\). Just because \(DE\) is the perpendicular bisector of \(AC\) does not imply any relationship between the lengths of \(BD\) and \(BE\)

Answer:

\(\overline{BD}\cong\overline{BE}\)