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Questions and Answers
What is the definition of a ray?
What is needed to properly name a ray?
How is an angle formed?
Which of the following units is used to measure an angle?
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What type of angle measures exactly 90 degrees?
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What do opposite rays share?
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What is true about congruent angles?
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What is the purpose of an angle bisector?
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Study Notes
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: ∠\angleâˆ
- 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\anglemâˆ
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
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Description
Explore the essential concepts of rays and angles in this geometry quiz. Learn how to define and identify rays, opposite rays, and angles, as well as how to measure them using a protractor. This quiz is an excellent way to test your understanding of foundational geometry principles.
