1. Bisectors in Triangles
Chapter 5 Section 2
Bisectors in Triangles
With your straight edge, draw line segment AB. Use your compass and straight edge to draw the perpendicular bisector of AB. Label the point of intersection D, and label one other point on the perpendicular bisector C.

2. Based on what you learned up to this point, what triangles can you draw from these points, and what can you say about their congruency?

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: If a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment.

5. EH is the perpendicular bisector of DG. Find DH and EG.
Example 1
EH is the perpendicular bisector of DG. Find DH and EG.
Can we say that DG is the perpendicular bisector of EH? Why or why not?

6. Distance from a point to a line is the length of the perpendicular segment from the point to the line.
Perpendicular to the exterior angle segment…
Distance from a point to a line,

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

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

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

10. What is the length of segment FD?

11. How far is K from EH?
How far is K from ED?
What can you conclude about EK?
Find measure of angle DEH.

12. Geometry Classwork - Page 267: 2,4,6-15, 18-25.
When you are done with classwork, have it checked, then proceed to Homework.
Geometry Homework (Due Mon after Thanksgiving break) Perpendicular and Angle Bisectors: 1-8, 11-30