Question

Explain how to use the Converse of the Alternate Interior Angles Theorem to construct a line parallel to a given line through a point not on the line.

Answer 1

Using the Converse of the Alternate Interior Angles Theorem involves creating congruent alternate interior angles via a transversal to construct a parallel line through a given point.

Step-by-step explanation:

To use the Converse of the Alternate Interior Angles Theorem for constructing a line parallel to a given line through a point not on the line, you would follow these steps:

1. Identify the given line and the point through which the parallel line must pass.
2. Draw a transversal through the point so that it intersects the given line, creating an angle.
3. Measure that angle and then use a protractor to replicate that angle on the opposite side of the transversal starting at the point where the parallel line is to be drawn.
4. Mark the angle you've created, then draw a line from the point through the marked angle.
5. If the angles are congruent, then by the Converse of the Alternate Interior Angles Theorem, the lines are parallel.

The theorem states that if the alternate interior angles formed by a transversal with two lines are congruent, the lines are parallel. Thus, when you replicate the angle on the other side, ensuring they are congruent, it confirms that the new line drawn is parallel to the original line.