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Complete the sentence.

The intersection of three lines can be:

A. a ray
B. a point
C. a triangle
D. a line segment

1 Answer

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Final answer:

The intersection of three lines in a two-dimensional context can result in a single point where all three lines cross, which corresponds to option B. a point. A ray, a triangle, or a line segment cannot result from the intersection of three lines since they either extend beyond a single point or are not points of intersection.

Step-by-step explanation:

The intersection of three lines refers to the point where all three lines meet. Keeping in mind the two scenarios provided:

  • If all three lines are parallel, they will not intersect at a single point but continue without ever crossing.
  • If all three lines are mutually perpendicular, they could potentially meet at a single point in space if their dimensions are considered.

However, in the context of the two-dimensional geometry typically studied in middle school, three lines can only intersect at a point if they all cross at the same location. Therefore, the correct answer to the question is B. a point.

A ray, a triangle, or a line segment cannot be the result of the intersection of three lines in a two-dimensional context because:

  • A ray is part of a line that extends infinitely in one direction from a starting point. It cannot result from the intersection of lines as it has to originate from a point.
  • A triangle is a three-sided polygon, and although it is formed by lines, it is not the intersection point of those lines.
  • A line segment is a part of a line that is bounded by two endpoints, but it is not a point of intersection either.

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