The document discusses the concepts of perpendicular and angle bisectors, highlighting the conditions for a point to be equidistant from two objects or sides of an angle. It includes the perpendicular bisector theorem, its converse, and the angle bisector theorem, along with related problems. Additionally, it addresses practical applications, such as determining locations for a t-shirt stand in a park.

1. 5-2
Perpendicular and Angle
Bisectors

2. A point is equidistant from two objects
if it is the same distance from the
objects

3. Perpendicular Bisector Theorem
If a point is on the perpendicular bisector of a
segment, then it is equidistant from the endpoints of
the segment

4. Converse of the Perpendicular Bisector Theorem

5. Problem 1: Using the Perpendicular Bisector
Theorem

7. Problem 2: Using a Perpendicular Bisector
A park director wants to build a T-shirt stand equidistant from
the Rollin’ Coaster and the Spaceship Shoot. What are the
possible locations of the stand? Explain.

8. Distance from a point to a line: the length of the
perpendicular segment from the point to the line
The distance is also the length of the shortest
segment from the point to the line.
In the figure the distances from A to line l and from B
to l are represented by the red segments.

9. Angle Bisector Theorem
If a point is on the bisector of an angle, then the point
is equidistant from the sides of the angle

10. Converse of the Angle Bisector Theorem
If a point in the interior of an angle is equidistant from
the sides of the angle, then the point is on the angle
bisector

11. Problem 3: Using the Angle Bisector Theorem