Understanding Perpendicular Bisector Theorem and Its Applications

The page introduces fundamental concepts about the perpendicular bisector theorem and demonstrates its practical application through detailed examples.

Definition: The perpendicular bisector theorem states that if a point lies on the perpendicular bisector of a segment, it is equidistant from the endpoints of that segment.

Example: In the given diagram, if QS is a perpendicular bisector of segment PR, and PS = 6.8, then RS must also equal 6.8 due to the theorem.

Highlight: When solving problems, look for these key indicators:

• Lines of congruence showing equal segments
• 90-degree angle marks indicating perpendicularity
• Given statements about perpendicular bisectors

Vocabulary:

• Perpendicular Bisector: A line that intersects a segment at its midpoint at a 90-degree angle
• Equidistant: Equal in distance from a given point
• Lines of Congruence: Markings that indicate equal measurements

Quote: "Use the Perpendicular Bisector Theorem when you're given that a line is the perpendicular bisector in the diagram and trying to find if a point is equidistant to another."