Geometry Chapter on Rays and Angles

Rays

• A ray is a portion of a line with one endpoint and all points extending to one side
• Named using two points, the first point must be the endpoint and the second point can be any other point on the ray
• A ray is denoted by placing an arrow above the two points Example: AB→\overrightarrow{AB}AB

Opposite Rays

• Two rays that share the same endpoint, are on the same line (collinear), and extend in opposite directions, forming a straight line
• AB→\overrightarrow{AB}AB and BA→\overrightarrow{BA}BA are opposite rays

Angles

• Formed by two non-collinear rays (sides) that share a common endpoint (vertex)
• Angle symbol: ∠\angle∠
• An angle can be named using three points: ∠ABC\angle ABC∠ABC where point B is the vertex
• An angle can also be named using a single number or a single letter: ∠1\angle 1∠1 or ∠A\angle A∠A

Measuring Angles

• Measured in degrees
• 1 degree is 1/360th of a turn around a circle
• Protractor can be used to measure angles
• Symbol for "measure of an angle" is m∠m\anglem∠

Classifying Angles

• Acute Angle: An angle with a measure less than 90 degrees
• Right Angle: An angle with a measure of 90 degrees
• Obtuse Angle: An angle with a measure greater than 90 degrees but less than 180 degrees
• Straight Angle: An angle with a measure of 180 degrees
• Reflex Angle: An angle with a measure greater than 180 degrees but less than 360 degrees

Angle Addition and Subtraction Postulate

• Angles can be divided into smaller parts
• The sum of the measures of the smaller parts is equal to the measure of the largest angle
• Part + Part = Whole
• Whole – Part = Part

Congruent Angles

• Angles that have the same degree measure
• Notation: ∠ABC≅∠DEF\angle ABC \cong \angle DEF∠ABC≅∠DEF

Angle Bisector

• A ray that divides an angle into two congruent angles
• BD→\overrightarrow{BD}BD bisects ∠ABC\angle ABC∠ABC then ∠ABD≅∠CBD\angle ABD \cong \angle CBD∠ABD≅∠CBD