Rays AB and AC form both a line and an angle because of their geometric properties related to their common endpoint and directions: Forming a Line:
- Rays AB and AC share the same endpoint A.
- If these rays extend in exactly opposite directions from A, they are called opposite rays.
- Opposite rays together form a straight line because they cover all points along a line passing through A, extending infinitely in both directions (toward B and toward C).
- Thus, rays AB and AC combine to form the line BC (or line CA/AB depending on naming), which is a straight path through points B, A, and C
Forming an Angle:
- An angle is defined as two rays sharing a common endpoint, called the vertex.
- Rays AB and AC share the endpoint A, which becomes the vertex of the angle.
- The two rays form angle BAC (or angle CAB), measured as the rotation from one ray to the other around point A.
- Since AB and AC are opposite rays, the angle they form is a straight angle measuring 180 degrees, representing a straight line but also an angle
Summary:
- Rays AB and AC form a line because as opposite rays, they extend infinitely in opposite directions along the same straight path.
- They form an angle because two rays with a common endpoint always create an angle at that vertex.
- In this case, the angle is a straight angle (180°) due to the rays being opposite
This dual nature arises from the definitions of rays, lines, and angles in geometry.
