What you’ll learn
Define and classify angles.
Key idea
A pair of rays defines one angle only when their endpoints coincide.
The starting endpoints must coincide; a crossing elsewhere or first angle letter does not define the shared vertex.
Worked example
Classify examples and non-examples for the concept 'Define and classify angles'.
Labeled coordinate diagram: ray AB from A=(-2, -2) through B=(0, -2), and ray AC from A through C=(0, 0). Do the two given rays form one angle? Classify with the defining feature.
- An angle consists of two rays sharing their starting endpoint.
- Vertex A; sides ray AB and ray AC — both begin at A=(-2, -2). Three-letter angle notation puts the vertex in the middle; intersections elsewhere do not change the rays given.
Answer: Yes — Vertex A; sides ray AB and ray AC — both begin at A=(-2, -2).
Quick Check
Classify examples and non-examples for the concept 'Define and classify angles'.
Labeled coordinate diagram: ray AB from A=(-2, -2) through B=(2, -2), and ray CD from C=(-2, 1) through D=(-4, 4). Do the two given rays form one angle? Classify with the defining feature.