Question

1. in this diagram, line segment cd is the perpendicular bisector of line segment ab. assume the conjecture that the set of points equidistant from a and b is the perpendicular bisector of ab is true. is point e closer to point a, closer to point b, or the same distance between the points? explain how you know. ab ⊥ cd

Explanation:

Step1: Recall the property

The set of points equidistant from A and B is the perpendicular bisector of AB.

Step2: Analyze point E's position

Point E is not on the perpendicular bisector CD of AB.

Step3: Determine the distance

Points on the perpendicular bisector are equidistant from A and B. Since E is not on it, it is closer to either A or B. By visual inspection (or using the fact that we can draw right - angled triangles and apply the Pythagorean theorem), we can see that E is closer to A.

Answer:

Point E is closer to point A.