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Questions and Answers
What must be true about the two points used to name a ray?
Which of the following best describes opposite rays?
Which unit is used to measure angles?
What determines an angle's classification as acute, right, or obtuse?
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If an angle bisector divides an angle into two congruent angles, what can be said about their measures?
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Which equation represents the Angle Addition Postulate?
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What is the measure of an angle that measures 100°, after being bisected?
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What is the symbol for the measure of an angle?
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Study Notes
Ray
- A ray is part of a line consisting of one endpoint and all points to one side of the endpoint.
- A ray is like a "half" line.
Naming Rays
- Use two points.
- The first point must be the endpoint.
- The second point can be any other point on the ray.
- Place a small arrow above the two points.
Opposite Rays
- Opposite rays have the same endpoint, are on the same line (collinear), and extend in opposite directions.
- Opposite rays form a straight line.
Angle
- An angle is formed by two intersecting rays that share a common endpoint (vertex) and are not on the same line.
- The two rays are called the sides of the angle.
Naming Angles
- An angle is named using three letters, with the vertex in the middle.
- An angle can also be named by the vertex letter alone.
Measuring Angles
- Angles are measured in degrees.
- One degree is equal to 1/360th of a circle.
- A protractor can be used to measure angles.
- The symbol for "measure of an angle" is a small "m" written before the angle name.
Classifying Angles
- Acute Angle: Less than 90 degrees
- Right Angle: Exactly 90 degrees
- Obtuse Angle: Greater than 90 degrees and less than 180 degrees
- Straight Angle: Exactly 180 degrees
- Reflex Angle: Greater than 180 degrees and less than 360 degrees
Angle Addition/Subtraction Postulate
- The angles can be divided into smaller parts.
- The measure of the larger angle is equal to the sum of the measures of the smaller angles.
- Part + Part = Whole
- Whole - Part = Part.
Congruent Angles
- Congruent angles have the same degree measure.
- The symbol for congruent angles is an equal sign with a small "tilde" above it.
Angle Bisector
- A ray that divides an angle into two congruent angles.
Example 4
- Ray RT bisects ∠QRS. If m∠QRS = 100°, then m∠QRT = 50°.
- Ray YA bisects ∠XYZ. If m∠XYA = 24°, then m∠XYZ = 48°.
- Ray BD bisects ∠EBC.
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Description
This quiz covers the concepts of rays and angles in geometry. It includes naming rays and angles, as well as the definitions and properties of opposite rays and angle measurement. Test your understanding of these fundamental geometric principles.
