Geometry, Please Help!

Question

Diagram Link: https://assets.learnosity.com/organisations/154/3e767868-ea7d-4cee-93af-51abb4809055.png

Line segment CD is the perpendicular bisector of line segment CB.

Is line segment AB the perpendicular bisector of line segment CD? Why or why not?

Answer 1

The diagram shows that AB and CD are perpendicular because their intersection at point M forms a right angle. CD is given as the perpendicular bisector of AB, meaning that point M is the midpoint of AB. However, point M is not necessarily the midpoint of segment CD, and it certainly does not look like the midpoint of CD in the diagram and no additional information is provided to indicate that M is the midpoint of CD. So the answer is No, AB is not the perpendicular bisector of CD because point M is not the midpoint of CD.