1. Perpendicular Bisector of a Segment and Angle Bisector
Geometry
Mr. Zampetti
Unit 2, Day 2
Notes adapted from:
Photos from:

2. Definition
Bisect - To cut into two congruent (equal) pieces.

3. Constructing a Perpendicular Bisector
You will be given a segment that looks similar to this:
A B

4. Constructing a Perpendicular Bisector
Step 1: Place your compass point on A and stretch the compass MORE THAN half way to point B.

5. Constructing a Perpendicular Bisector
Step 2: Swing a large arc that will go BOTH above and below the segment

6. Constructing a Perpendicular Bisector
Step 3: Without changing the compass, place the compass point on B and swing the arc again.  **The two arcs should intersect**

7. Constructing a Perpendicular Bisector
Step 4: With your straightedge, connect the two points of intersection

8. This is what it will look like:

9. Watch the video!
Regentsprep.org

11. Now practice…

12. Constructing an Angle Bisector
You will be given an angle that looks similar to this: B A C

13. Constructing an Angle Bisector
Step 1: Place the point of the compass on the vertex (point A)
Step 2: Stretch the compass to any length as it stays ON the angle

14. Construction an Angle Bisector
Step 3: Swing an arc so the pencil crosses both sides of the angle.  This will create two intersection points with the sides (rays) of the angle.
Step 4: Place the compass point on one of these new intersection points and while staying between the sides of the angle, place an arc in this interior

15. Construction an Angle Bisector
Step 5: Without changing the width of the compass, place the point of the compass on the other intersection point and make the same arc.  **Your two small arcs in the interior of the angle should be crossing**
Step 6: Connect the point where the two small arcs cross to the vertex of the angle (point A)

16. This is what it will look like:

17. Watch the video!
Regentsprep.org

19. Now practice…