Perpendicular Bisector of a Segment and Angle Bisector

GeometryMr. ZampettiUnit 2, Day 2

Notes adapted from: http://www.regentsprep.org/Regents/math/geometry/math-GEOMETRY.htmPhotos from: http://www.wikihow.com/

Definition

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

Constructing a Perpendicular Bisector

• You will be given a segment that looks similar to this:

A B

Constructing a Perpendicular Bisector

• Step 1: Place your compass point on A and stretch the compass MORE THAN half way to point B.

Constructing a Perpendicular Bisector

• Step 2: Swing a large arc that will go BOTH above and below the segment

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**

Constructing a Perpendicular Bisector

• Step 4: With your straightedge, connect the two points of intersection

This is what it will look like:

Watch the video!

Regentsprep.org

Now practice…

Constructing an Angle Bisector

• You will be given an angle that looks similar to this:

B

A C

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

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

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)

This is what it will look like:

Watch the video!

Regentsprep.org

Now practice…