Question

line cd is the perpendicular bisector of segment ab. the lines intersect at point e. which of these statements is true? a e is closer to a. b e is closer to b. c e is the same distance from a and b. d there is not enough information to be sure.

Explanation:

Step1: Recall property of perpendicular bisector

A perpendicular bisector of a line - segment divides the segment into two equal parts and is perpendicular to it. Any point on the perpendicular bisector of a line - segment is equidistant from the endpoints of the line - segment.

Step2: Analyze point E

Since line CD is the perpendicular bisector of segment AB and they intersect at point E, by the property of the perpendicular bisector, point E is equidistant from A and B.

Answer:

C. E is the same distance from A and B.