Which theorem or postulate is the construction of parallel lines based upon?
A. Consecutive Interior Angles Converse Theorem
B. Corresponding Angles Converse Postulate
C. In the same plane, if two lines are perpendicular to the same line, then they are parallel to each other.
D. Alternate Interior Angles Converse Theorem
I'd say C
The construction of parallel lines is based on the third option:
C. In the same plane, if two lines are perpendicular to the same line, then they are parallel to each other.
The construction of parallel lines is based on the theorem known as the "Corresponding Angles Converse Postulate."
To understand this theorem and how it relates to the construction of parallel lines, we need to consider the properties of angles formed when two lines are intersected by a transversal (a line that intersects two or more other lines).
The corresponding angles are formed when the transversal cuts through the two given lines. These angles are positioned in such a way that they are on the same side of the transversal and in corresponding (or matching) positions.
The Corresponding Angles Converse Postulate states that if two lines are intersected by a transversal and corresponding angles are congruent (or equal), then the lines are parallel.
In other words, if we are given two lines and a transversal that intersects them, and we find that the corresponding angles formed by the transversal are congruent, we can conclude that the two lines are parallel.
So, the correct answer to the question is B. Corresponding Angles Converse Postulate.