1. 5.1: Perpendicular Bisectors
GEOMETRY: Chapter 5
5.1: Perpendicular Bisectors

2. A segment, ray, line, or plane that is perpendicular to a segment at its midpoint is called a perpendicular bisector.
A point is equidistant from two figures if the point is the same distance from each figure. Points on the perpendicular bisector of a segment are equidistant from the segment’s endpoints.
Draw and explain an example.

3. Theorem 5.1: Perpendicular Bisector Theorem
In a plane, if a point is one the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.
Images taken from: Geometry. McDougal Littell: Boston, P. 303.

4. Theorem 5.2: Converse of the Perpendicular Bisector Theorem
In a plane, if a point is equidistant from the endpoints of the segment, then it is on the perpendicular bisector of a segment.
Images taken from: Geometry. McDougal Littell: Boston, P. 303.

5. Ex. 1: 27
Images taken from: Geometry. McDougal Littell: Boston, P. 304

6. Ex. 2:
Images taken from: Geometry. McDougal Littell: Boston, P. 304.

7. Ex. 2:
Images taken from: Geometry. McDougal Littell: Boston, P. 304.

8. Theorem 5.3: Angle Bisector Theorem If a point is on the
bisector of an angle,
then it is equidistant
from the two sides
of the angle.
Image taken from: Geometry. McDougal Littell: Boston, P. 310.

9. Theorem 5.4: Converse of the Angle Bisector Theorem
If a point is in the interior
of an angle and is
equidistant from the
sides of the angle, then it
lies on the bisector of an angle.
Image taken from: Geometry. McDougal Littell: Boston, P. 310.

10. Ex. 3: Find the measure of angle BAD.
Images taken from: Geometry. McDougal Littell: Boston, P. 311.

11. Ex. 4: Three spotlights form two congruent angles
Ex. 4: Three spotlights form two congruent angles. Is the actor closer to the spotted area on the right or on the left?
Images taken from: Geometry. McDougal Littell: Boston, P. 311.

12. Ex. 5: For what value of x does P lie on the bisector of angle A?
Images taken from: Geometry. McDougal Littell: Boston, P. 311.

13. 5.1, p. 269, #1-13 odds, all