Geometry: Rays and Angles

Ray

• A part of a line that has one endpoint and extends infinitely in one direction.

Naming Rays

• Use two points
  • First point must be the endpoint.
  • Second point can be any other point on the ray.
• Place a small arrow above the two points.
  • The arrow points in the direction the ray extends.

Opposite Rays

• Two rays that share the same endpoint and lie on the same line, extending in opposite directions.
  • They form a straight line.

Angle

• Formed by two rays that share a common endpoint called the vertex.
• The two rays are called the sides of the angle.

Naming Angles

• Three ways to name an angle:
  • By its vertex (e.g., ∠A)
  • By three points (e.g., ∠BAC, where B and C are points on each side of the angle, and A is the vertex)
  • By a number (e.g., ∠1)

Angle Measure

• Measured in units called degrees (°)
  • 1 degree = 1/360th of a full circle.
• Protractors can be used to measure angles.
• Symbol for "measure of an angle" is "m∠".

Types of Angles

• Acute angle: Angle with measure less than 90°
• Right angle: Angle with measure exactly 90°
• Obtuse angle: Angle with measure greater than 90° but less than 180°
• Straight angle: Angle with measure exactly 180°
• Reflex angle: Angle with measure greater than 180° but less than 360°

Angle Addition Postulate

• Angles can be divided into smaller parts.
• The sum of the smaller angles equals the measure of the larger angle.
  • Part + Part = Whole
  • Whole - Part = Part

Congruent Angles

• Angles that have the same degree measure.
• Notation: ≅

Angle Bisector

• A ray that divides an angle into two congruent angles.
• The ray must pass through the vertex and lie within the angle.

This quiz covers the fundamental concepts of rays and angles in geometry. You'll learn how to name rays and angles, understand opposite rays, and measure angles using degrees. Test your knowledge of these essential geometric principles.