Geometry

Question Analysis

The main focus is using the equal - length markings () and the perpendicular at  to apply the properties of a perpendicular bisector and find the length of .

 

Key Concept Explanation

A perpendicular bisector of a line segment is a line that is perpendicular to the segment and divides it into two equal parts. When a point () is equidistant from the endpoints of a line segment ( and ) and there is a perpendicular line () to that segment,  is the perpendicular bisector of . Points on the perpendicular bisector are equidistant from the endpoints of the bisected segment, and the perpendicular bisector splits the segment into two congruent sub - segments.

 

Step - by - Step Solution

1. Since  and , we can conclude that  is the perpendicular bisector of .

By the property of the perpendicular bisector, it divides  into two equal parts. So,

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