This page delves into angle bisector theorems and their applications in solving geometric problems, including coordinate geometry.

Definition: An angle bisector is a ray that divides an angle into two equal parts.

Highlight: The angle bisector theorem states that any point on an angle bisector is equidistant from the sides of the angle.

Example: Problem 8 shows solving for x using the equation 4x+30=9x-5, yielding x=7.

Quote: "If a point is on the interior of an angle and equidistant from the sides of the angle, then the point is on the angle bisector."

The page includes advanced applications involving coordinate geometry and angle measurements, demonstrating how to verify points lying on perpendicular bisectors using distance formulas.

This page introduces fundamental concepts of perpendicular bisectors and their properties in geometry. The content focuses on practical problem-solving using these theorems.

Definition: A perpendicular bisector is a line that intersects a segment at a 90-degree angle and divides it into two equal parts.

Highlight: The perpendicular bisector theorem states that any point on the perpendicular bisector is equidistant from the endpoints of the segment it bisects.

Example: Problem 1 demonstrates finding x using the equation 13x-48=7x+24, resulting in x=12 through algebraic manipulation.

Vocabulary: Equidistant means having equal distances from a given point or line.

The page includes multiple practice problems involving finding segment lengths and x-values using algebraic equations derived from geometric relationships.