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)

a) Definition: An Angle is two coplanar Rays with a common former Endpoint. (Contradiction is described in the image)

b) Undefined Terms can generate Angles in the following ways:

(i) Angles are either generated by three distinct Points, not necessarily collinear.

(ii) Or a Line and an non-collinear Point,

(iii) Or two Planes with a common Line of intersection and each of them with a proper Point.

a) If we consider the definition of Angle as two collinear Rays with a common Endpoint. Then, we can find the following two contradictions: (i) The latter Endpoint of the first Ray coincides the former Endpoint of the second Ray, as we can see in the figure attached below, when Angles are formed by two Rays with the same former Endpoint; (ii) Angles are not necessarily collinear but always coplanar, given that a Plane is generated by the existence of three non-collinear Points.

Hence, a more accurate definition for Angle could be: An Angle is two coplanar Rays with a common former Endpoint.

b) There are three Undefined Terms in Geometry: (i) Point, (ii) Line, (iii) Plane, all three are related to each other and can be described only by its attributes. In this case, these Undefined Terms can generate Angles in the following ways:

(i) Angles are either generated by three distinct Points, not necessarily collinear.

(ii) Or a Line and an non-collinear Point,

(iii) Or two Planes with a common Line of intersection and each of them with a proper Point.

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