Sign In
Based on the characteristics of the diagram, the following relation holds true.
AS=BS=CS
Assume that ABC is a triangle and DS, ES, and FS are the perpendicular bisectors of the sides of this triangle.
Notice that S is a point on the perpendicular bisector of AB. Therefore, by the Perpendicular Bisector Theorem, S is equidistant from A and B.
Similarly, S is also a point on the perpendicular bisector of BC. Using the Perpendicular Bisector Theorem once again, it can be concluded that S is equidistant from B and C.
The proof can be summarized in the following two-column table.
Statements | Reasons |
ABC is a triangleDS is a perpendicular bisector of ABES is a perpendicular bisector of BCFS is a perpendicular bisector of AC
|
Given |
AS=BSBS=CS
|
Perpendicular Bisector Theorem |
AS=CS | Transitive Property of Equality |