Angle Bisector and Addition Postulates, Types of Angles

Angle Addition Postulate : if two angles are adjacent then their sum is equal to the outer angle.

A

B C

D

ABD + DBC = ABC

Acute angle : is greater than 0 degrees and less than 90 degrees

Right angle is always 90 degrees.

Obtuse angle is greater than 90 degrees and less than 180 degrees.

Symbol means 90 degrees

Straight angle is 180 degrees.

Midpoint of a Segment : divides a segment into two congruent parts. ( two equal lengths )A B C

Point B divides AC into two congruent parts

Perpendicular Lines : are lines that intersect at 90 degrees.

Symbol

Perpendicular Bisector : is a line that divides a segment into two congruent parts at 90 degrees.

midpoint

90 degrees

Congruent Segments

Angle Bisector : is a ray that divides an angle into two congruent parts.

Angle bisector

symbol for congruent angles

The angle was divided into two equal sizes.

Ray BD is the angle bisector of the angle ABC. If angle ABD is (2x – 4) degrees and angle ABC is (6x – 42)° , how any degrees is angle DBC ?

A

B

D

C

Angle DBC = 30 degrees

If the line PS is the perpendicular bisector of the segment CD. MD is (3x – 1)cm. and CD is (7x – 17)cm, what is the length of CM ?

Solution

C M D

P

S

Problem

• What are the different ways you can name this angle?

D

A

Y

DAY or YAD