Introduction to Angles

2.5 What is an Angle?

An angle is formed by two rays having a common starting point.

• Vertex: The common starting point (e.g., point $B$).
• Arms: The two rays forming the angle (e.g., $\overrightarrow{BD}$ and $\overrightarrow{BE}$).

Naming an Angle

We can name an angle in three ways:

1. Using the vertex letter: Angle B or $\angle B$.
2. Using three letters with the vertex in the middle: Angle DBE or $\angle DBE$.
3. Alternatively: Angle EBD or $\angle EBD$.

2.6 Comparing Angles (Size as Rotation)

The size of an angle is not the length of its arms. Instead, it is the amount of rotation or turn needed about the vertex to move the first ray to the second ray.

• Imagine opening a book cover. The more you rotate the cover, the larger the angle.
• Imagine the blades of scissors opening. Wider opening = Larger angle.

Superimposition

We can compare two angles by placing one over the other (superimposition).

1. Place the vertices together.
2. Align one arm of the first angle with one arm of the second.
3. Check where the other arm falls.

• If the arms overlap completely, the angles are equal.
• If the arm of the second angle falls “outside” the first, the second angle is greater.