Question

Segment _AB is the perpendicular bisector of _CD at point M.

Which statement is always true?
(1) _CB= _DB
(2) _CD= _AB
(3) ACD - BCD
(4) ACM - BCM

Answer 1

Explanation:

Since segment AB is the perpendicular bisector of CD, it means that point M is the midpoint of segment CD and the two line segments MC and MD are congruent.

Therefore, we can conclude that statement (1) is always true: CB = DB, as both segments are congruent to MC and MD, respectively.

Statements (2), (3), and (4) are not necessarily true based on the information given.