1.5 Segment and Angle Bisectors

Goal 1: Bisect a segment

Goal 2: Bisect an angle

CAS 16, 17

Midpoint

A midpoint of a segment is the point that divides or bisects the segment into two congruent segments.

A BM

MBAM

Congruent Marks and Congruent Arcs

Small red marks used to identify congruent segments.

A BM

Segment Bisector

A segment bisector is a segment, ray, line, or plane that intersects a segment at its midpoint

A BM

Line MN is the bisector

N

Construction

A construction is a geometric drawing that uses a limited set of tools, usually a compass and a straight edge.

Midpoint Formula

If A(x1,y1) and B(x2,y2) are points in a coordinate plane, then the midpoint of AB has coordinates

2,

22121 yyxx

(4, -1)

(-2, 4)

)2

3,1(

Angle Bisector

An angle bisector is a ray that divides an angle into two adjacent angles that are congruent.

C

A

D

B

BCDmACDm