# Basics of Triangle: Angle bisector

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This pdf includes the following topics:-
Midpoint
Segment bisector
The Midpoint Formula
Bisecting an Angle
1. Chapter 1
Basics of Geometry
2. Section 5
Segment and Angle Bisectors
3. The __midpoint__ of a segment is the point that divides, or __bisects__, the
segment into two congruent segments. In this book, matched red congruence
marks identify congruent segments in diagrams.
A __segment bisector__ is a segment, ray, line, or plane that intersects a
segment at its midpoint.
C
A M B A M B
D
M is the midpoint of AB if
M is on AB and AM = MB. CD is a bisector of AB.
4. You can use a compass and a straightedge (a ruler without marks) to
construct a segment bisector and midpoint of AB. A construction is a
geometric drawing that uses a limited set of tools, usually a compass
and a straightedge.
5. If you know the coordinates of the endpoints of a segment, you can calculate
the coordinates of the midpoint. You simply take the mean, or average, of the
x-coordinates and of the y-coordinates. This methods is summarized as the
Midpoint Formula.
6. The Midpoint Formula
If A(x1, y1) and B(x2, y2) are points
in a coordinate plane, then the
midpoint of AB has coordinates
 x1  x 2 y1  y 2 
 , 
 2 2 
7. Example 1: Finding the Coordinates of the Midpoint of a Segment
Find the coordinates of the midpoint of AB with endpoints
A(-2, 3) and B(5, -2).
8. Example 2: Finding the Coordinates of an Endpoint of a Segment
***TEST***
The midpoint of RP is M(2, 4). One endpoint is R(-1, 7). Find the coordinates of
the other endpoint.
9. GOAL 2: Bisecting an Angle
A
An angle bisector is a ray that divides an
angle into two adjacent angles that are
D
congruent. In the diagram at the right, the C
ray CD bisects angle into two congruent angles, and In this book, matching congruence arcs
identify congruent angles in diagrams.
10. Example 3: Dividing an Angle Measure in Half
The ray FH bisects the angle m H
F
120°
120/2 = 60
m m
11. Example 4: Doubling an Angle Measure
K
In the kite, two angles are bisected. 45°
E I
Find the measure of the two angles.
m m
12. Example 5: Finding the Measure of an Angle
In the diagram, RQ bisect of the two congruent angles are (x + 40)° and
(3x – 20)°. Solve for x.
(x + 40)° Q
R
(3x – 20)°
S