Angles. Degree Measure of an Angle
Углы. Градусная мера угла
1. Definition of an Angle (Определение угла)
Definition: An angle is a geometric figure formed by two rays (called the sides of the angle) that share a common endpoint (called the vertex of the angle).
- Sides of the angle (стороны угла): The two rays that form the angle.
- Vertex of the angle (вершина угла): The common endpoint where both rays begin.
In the diagram to the right, rays BA and BC are the sides, and point B is the vertex.
Interactive visualization — available in the full lesson
2. Notation of Angles (Обозначение углов)
Ways to Name an Angle:
| Method | Example | Rule |
|---|---|---|
| Three letters | ∠ABC | Vertex letter always in the middle |
| Single letter | ∠B | Only when no confusion (one angle at vertex) |
| Greek letters | ∠α, ∠β, ∠γ | Placed inside the angle arc |
| Numbers | ∠1, ∠2, ∠3 | Placed inside the angle arc |
⚠️ Common Mistake: When using three letters, the vertex must be the middle letter. Writing ∠BAC instead of ∠ABC refers to a different angle (with vertex at A)!
✅ Correct: ∠ABC — vertex is B
❌ Wrong: ∠BAC — this means vertex is A!
❌ Wrong: ∠BAC — this means vertex is A!