Question

Compare the two statements below and decide if the phrase: "In a plane," needs to be included in order to make a true statement.

1. In a plane, if a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other line.

versus

2. If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other line.





answer choices:

A) It does not need to be included. By leaving it out of the statement, the reader considers three dimensions not just the xy-plane. The two parallel lines would determine a plane. However, the transversal could intersect only one of the lines. This would allow the proof to use the Corresponding Angles Theorem.


B) It does not need to be included. By leaving it out of the statement, the reader considers three dimensions not just the xy-plane. The two parallel lines would determine a plane. However, the transversal could intersect only one of the lines. This would allow the proof to use the Angle Bisector Theorem.


C) It needs to be included as it forces the reader to consider only two dimensions, like the xy-plane. The two parallel lines would determine the plane and the transversal would intersect both lines. This would allow the proof to use the Corresponding Angles Theorem.


D) It needs to be included as it forces the reader to consider only two dimensions, like the xy-plane. The two parallel lines would determine the plane and the transversal would intersect both lines. This would allow the proof to use the Angle Bisector Theorem.

Answer 1

The phrase "In a plane," is necessary to ensure that the context is two-dimensional Euclidean geometry, where the Corresponding Angles Theorem indicates that a transversal perpendicular to one parallel line must also be perpendicular to another.

Step-by-step explanation:

The correct answer to whether the phrase "In a plane," needs to be included for a statement to be true is C. The phrase needs to be included because it restricts the context to two dimensions, which is essential when talking about parallel lines and transversals in Euclidean geometry. By stating "In a plane," it is ensured that the two parallel lines define that plane, and any transversal that is perpendicular to one of these lines will also be perpendicular to the other. This follows from the Corresponding Angles Theorem, which implies that alternate interior angles are equal when a transversal intersects two parallel lines in a plane. When one of these angles is a right angle, so is the corresponding angle, confirming that the transversal is perpendicular to both lines.

Answer 2

by any chance do you go to a higl school in Conroe bc I’m taking that exact test on canvas

Step-by-step explanation: