Part A: An angle is two collinear rays with a common endpoint. Find an example that contradicts this definition. How would you change the definition to make it more accurate? (5 points) Part B: Give an example of an undefined term and how it pertains to angles. (5 points)

If the rays are collinear, then we have two options:

1) Each ray points in a different direction, then the two rays form a line.

2) The two rays point in the same direction, then they share all their points.

This second one is the contradiction, because this is equivalent to having a single ray, and we can not define an angle with a single ray.

To have an angle, we must have two NON-colinear rays that share the same endpoint. Where the endpoint is the vertex of the angle. And we could add something kinda trivial, the two rays must be in the same plane in where we are measuring the angle.

Because we also could have two rays that start in the (0,0), and one goes along the positive x-axis and the other along the positive z-axis.

If we look this in the plane x-y, then we will only see the ray that goes along the x-axis and we could not measure an angle in the plane x-y, then is useful to ask that the two rays also must be in the same plane.

b) An undefined term is "plane" and it is related to angles becuase it basically tells what we are looking to measure, the plane is the first thing we need to define. And then look at the rays in the already defined plane.