Fundamental Concepts
14. The Angle's Birth · where two rays meet at a vertex
Two rays from a common vertex always form an angle.
An angle is a geometric figure formed by two rays (or lines, or line segments) that share a common endpoint, known as the vertex. It measures the rotation or "opening" between the two sides, usually in degrees (°) or radians.
What this lesson covers
Try to break it
What happens if A and B line up perfectly with O? The angle disappears or becomes a straight line!
How you build it
Make an angle at vertex O.
- Place vertex O — the common starting point of both rays.
- Place point A to mark the direction of the first ray.
- Draw ray OA (Ray tool: O then A).
- Place point B in a different direction from O.
- Draw ray OB (Ray tool: O then B). The two rays meeting at O form angle ∠AOB.
The proof, step by step
Verify that the angle measure updates as you drag the rays.
- Identify the common starting point of the two rays.
- Name the two rays extending from the point.
- Recognize the space between the rays as the angle.
- Combine these to define an angle.
Worked example
Two different rays starting from the same fixed point form an angle. What is the name of this fixed point?
The fixed point where the two rays meet is called the vertex of the angle.
- Vertex — correct
- Center
- Origin
- Intersection