Understanding Rays and Angles

Rays and Vertices

• Example: Ray starting at point A, passing through B (ray AB)
• Another ray from A through C (ray AC)
• Common vertex: both rays have vertex at A

Definition of an Angle

• Formed by two rays with the same vertex
• Geometric definition: two rays sharing a common vertex

Naming the Angle

• Symbol for angle: ∠
• Example: ∠BAC or ∠CAB (Common vertex A in the middle)
• Important to specify three points to indicate the angle clearly

Common Vertex Ambiguities

• Angle defined by multiple intersecting line segments
• Example: line segment DE and FG intersecting at point H
• Various angles at vertex H (e.g., ∠EHG, ∠GHE, ∠DHG, ∠GHD, ∠FHE, ∠EHF, ∠FHD, ∠DHF)

Measuring Angles

• Angles differ in how open they are
• Example: ∠BAC appears more closed compared to ∠XYZ
• Measure of an angle related to how open or closed it is
• Further details on measuring angles to be covered in subsequent content