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Part A: Consider the statement “An angle is two collinear rays with a common endpoint.” Describe an example that contradicts this statement. How could you change the statement to make it an accurate definition of an angle?

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Final answer:

An accurate definition of an angle is two non-collinear rays that have a common endpoint, not collinear rays. The provided statement was incorrect and has been corrected to reflect the true nature of an angle in geometry.

Step-by-step explanation:

The given statement "An angle is two collinear rays with a common endpoint" is incorrect because an angle is actually formed by two non-collinear rays sharing a common endpoint, not collinear rays. Collinear rays would not create an angle, as they would lie on the exact same line. An example that contradicts this statement is simply any common angle we see in geometry, such as the corners of a square or a triangle; none of the sides of these shapes are collinear where they meet.

To correct the statement and provide an accurate definition of an angle, it should be revised to: "An angle is formed by two non-collinear rays that have a common endpoint." This new definition encapsulates the idea that an angle measures the amount of turn between the two rays.

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